id int64 1 141k | title stringlengths 15 150 | body stringlengths 45 28.5k | tags stringlengths 1 102 | label int64 1 1 | text stringlengths 128 28.6k | source stringclasses 1
value |
|---|---|---|---|---|---|---|
44,540 | Karloff's algorithm applied to sparse graphs | <p>I'm given a graph $G = (V, E)$ with $|V| = N$ and $|E| = m \ge N^{1+c}$ edges for some constant $c >0$. $G$ is called a $c$-dense graph. </p>

<p>Karloff [1, p.6] has given a map-reduce algorithm called "Finding an MST of a Dense Graph Using Map-Reduce" which finds an MST of $G$ by randomly partiti... | algorithms search algorithms parallel computing spanning trees mapreduce | 1 | Karloff's algorithm applied to sparse graphs -- (algorithms search algorithms parallel computing spanning trees mapreduce)
<p>I'm given a graph $G = (V, E)$ with $|V| = N$ and $|E| = m \ge N^{1+c}$ edges for some constant $c >0$. $G$ is called a $c$-dense graph. </p>

<p>Karloff [1, p.6] has given a map-redu... | habedi/stack-exchange-dataset |
44,542 | How to prove that the probability that a random graph has a stable set of size $2\lceil \log n\rceil$ is sub-constant? | <p>Given a random graph on $n$ vertices where each edge is included with probability $1/2$. Lets call it $G=(n,1/2)$. How can we show that the probability that this graph has a stable set of size at least $2\lceil \log n\rceil$ is sub-constant?</p>
 | graphs | 1 | How to prove that the probability that a random graph has a stable set of size $2\lceil \log n\rceil$ is sub-constant? -- (graphs)
<p>Given a random graph on $n$ vertices where each edge is included with probability $1/2$. Lets call it $G=(n,1/2)$. How can we show that the probability that this graph has a stable set o... | habedi/stack-exchange-dataset |
44,546 | Getting the sorted sequence from a level-wise sorted min-heap | <p><img src="https://i.stack.imgur.com/AFaoU.png" alt="enter image description here">
A <em>heap sorted by levels</em> is a heap which:</p>

<ol>
<li><p>Every parent is smaller than its children.</p></li>
<li><p>The nodes in each level are sorted from the smallest to the greatest.</p></li>
</ol>... | algorithms data structures sorting heaps | 1 | Getting the sorted sequence from a level-wise sorted min-heap -- (algorithms data structures sorting heaps)
<p><img src="https://i.stack.imgur.com/AFaoU.png" alt="enter image description here">
A <em>heap sorted by levels</em> is a heap which:</p>

<ol>
<li><p>Every parent is smaller than its children.<... | habedi/stack-exchange-dataset |
44,552 | Properties of Reverse Polish Notation expressions that are algebraically invariant | <p>The RPN expressions</p>

<pre><code>a b + c *
</code></pre>

<p>and</p>

<pre><code>f d e + *
</code></pre>

<p>are algebraically equivalent, though the names of the variables are different and the order of evaluation is slightly different. The expressions</p>

<pre><c... | notation computer algebra equality | 1 | Properties of Reverse Polish Notation expressions that are algebraically invariant -- (notation computer algebra equality)
<p>The RPN expressions</p>

<pre><code>a b + c *
</code></pre>

<p>and</p>

<pre><code>f d e + *
</code></pre>

<p>are algebraically equivalent, though the n... | habedi/stack-exchange-dataset |
44,556 | In the Gas-Up problem, how is the amount of gas the same up to a cyclic shift regardless of starting city? | <p>I'm working through <em>Elements of Programming Interviews</em> as practice for finding a job. I've spent a ridiculous amount of time on Problem 18.7.</p>

<blockquote>
 <p>In the gas-up problem, $n$ cities are arranged on a circular road. You
 need to visit all of the $n$ cities and come back to t... | algorithms | 1 | In the Gas-Up problem, how is the amount of gas the same up to a cyclic shift regardless of starting city? -- (algorithms)
<p>I'm working through <em>Elements of Programming Interviews</em> as practice for finding a job. I've spent a ridiculous amount of time on Problem 18.7.</p>

<blockquote>
 <p>In the g... | habedi/stack-exchange-dataset |
44,562 | Time complexity of a vertical sweep algorithm with histogram computations | <p>In the paper</p>

<ul>
<li><a href="http://webdocs.cs.ualberta.ca/~nray1/MyWebsite/Papers/brain_tumor.pdf" rel="nofollow noreferrer">Quick Detection of Brain Tumors and Edemas: A Bounding Box Method
Using Symmetry</a>, Saha et al</li>
</ul>

<p>the authors claim that the running time of t... | time complexity image processing | 1 | Time complexity of a vertical sweep algorithm with histogram computations -- (time complexity image processing)
<p>In the paper</p>

<ul>
<li><a href="http://webdocs.cs.ualberta.ca/~nray1/MyWebsite/Papers/brain_tumor.pdf" rel="nofollow noreferrer">Quick Detection of Brain Tumors and Edemas: A Bounding Box M... | habedi/stack-exchange-dataset |
44,563 | Has this model of random directed graphs been studied? | <p>Youtube recently added a feature called autoplay, where each clip is assigned a (presumably related) clip that follows it. This, in effect, defines a directed graph on the set of youtube clips, where each vertex has outdegree 1. The user starts at a vertex of his choice and takes a walk along this graph.</p>
&#x... | random graphs network analysis | 1 | Has this model of random directed graphs been studied? -- (random graphs network analysis)
<p>Youtube recently added a feature called autoplay, where each clip is assigned a (presumably related) clip that follows it. This, in effect, defines a directed graph on the set of youtube clips, where each vertex has outdegree ... | habedi/stack-exchange-dataset |
44,568 | What is the reason of using Gaussian model for Background Modeling? | <p>I am a new learner to Background Subtraction (Background Modeling) and I am reading a few previous works on how it is performed. Starting with Wikipedia (by searching "Background Subtraction"), I could understand the first few simple methods, until the part "Running Gaussian average". I simply have no idea why a Gau... | image processing computer vision modelling | 1 | What is the reason of using Gaussian model for Background Modeling? -- (image processing computer vision modelling)
<p>I am a new learner to Background Subtraction (Background Modeling) and I am reading a few previous works on how it is performed. Starting with Wikipedia (by searching "Background Subtraction"), I could... | habedi/stack-exchange-dataset |
44,571 | How can the Operating System run on the same chip it is supposed to be managing? | <p>From my readings about Operating Systems (reading the basic material on Wikipedia, tech sites, etc) I've learned that the Operating System is a program that allows programs and applications to interact with the hardware in an efficient and safe way.</p>

<p>However I'm confused about how the Operating System... | operating systems | 1 | How can the Operating System run on the same chip it is supposed to be managing? -- (operating systems)
<p>From my readings about Operating Systems (reading the basic material on Wikipedia, tech sites, etc) I've learned that the Operating System is a program that allows programs and applications to interact with the ha... | habedi/stack-exchange-dataset |
44,574 | Existence of shortest path in a graph with no negative cycles? | <p>Suppose that the input graph $G$ does not have any negative cycles but however it is permitted to contain edges having negative weight. Let $s$ be the source vertex.</p>

<p>How do I prove that for every vertex $v$ in $G$, there is a shortest $s-v$ path with $<= n - 1$ edges?</p>

<p>Where $n$ is ... | graphs shortest path weighted graphs | 1 | Existence of shortest path in a graph with no negative cycles? -- (graphs shortest path weighted graphs)
<p>Suppose that the input graph $G$ does not have any negative cycles but however it is permitted to contain edges having negative weight. Let $s$ be the source vertex.</p>

<p>How do I prove that for every ... | habedi/stack-exchange-dataset |
44,577 | Proving algorithm for removing nodes from a complete graph with two kinds of edges | <p>Lets say $G$ is complete undirected graph with a set of edges coloured either black or red. The problem is to find an algorithm answering if it is possible to remove a subset of nodes from $G$ in a way such that all black edges are gone, but for any two nodes in the set of removed nodes there was no red edge between... | algorithms graphs | 1 | Proving algorithm for removing nodes from a complete graph with two kinds of edges -- (algorithms graphs)
<p>Lets say $G$ is complete undirected graph with a set of edges coloured either black or red. The problem is to find an algorithm answering if it is possible to remove a subset of nodes from $G$ in a way such that... | habedi/stack-exchange-dataset |
44,583 | Inducing a context free grammar | <p>I have a file containing a subset of possible strings from a context free language. I am looking for a mechanism to induce the grammar from this information. Is that possible?</p>
 | context free formal grammars | 1 | Inducing a context free grammar -- (context free formal grammars)
<p>I have a file containing a subset of possible strings from a context free language. I am looking for a mechanism to induce the grammar from this information. Is that possible?</p>
 | habedi/stack-exchange-dataset |
44,587 | Finding the median in a heap | <p>Given a binary heap $H$, indexed in $[1..n]$, whose elements are integers, is there a way to quickly find its <a href="https://en.wikipedia.org/wiki/Median" rel="nofollow">median</a> in $O(\log n)$-time?</p>
 | data structures priority queues selection problem | 1 | Finding the median in a heap -- (data structures priority queues selection problem)
<p>Given a binary heap $H$, indexed in $[1..n]$, whose elements are integers, is there a way to quickly find its <a href="https://en.wikipedia.org/wiki/Median" rel="nofollow">median</a> in $O(\log n)$-time?</p>
 | habedi/stack-exchange-dataset |
44,591 | Analysing Space Complexity | <p>I have to compute the space complexity of this function:</p>

<pre><code>double foo(int n){
 int i;
 double sum;
 if(n==0) return 1.0;
 else
 for(i=0;i<n;i++)
 sum+= foo(i);
 return sum 
}
</code></pre>

<p>What I have d... | algorithms algorithm analysis space analysis | 1 | Analysing Space Complexity -- (algorithms algorithm analysis space analysis)
<p>I have to compute the space complexity of this function:</p>

<pre><code>double foo(int n){
 int i;
 double sum;
 if(n==0) return 1.0;
 else
 for(i=0;i<n;i++)
 sum+= f... | habedi/stack-exchange-dataset |
44,594 | Data compression using prime numbers | <p>I have recently stumbled upon <a href="http://searchdl.org/public/book_series/elsevierst/1/28.pdf">the following interesting article</a> which claims to efficiently compress random data sets by always more than 50%, regardless of the type and format of the data.</p>

<p>Basically it uses prime numbers to uni... | information theory data compression primes | 1 | Data compression using prime numbers -- (information theory data compression primes)
<p>I have recently stumbled upon <a href="http://searchdl.org/public/book_series/elsevierst/1/28.pdf">the following interesting article</a> which claims to efficiently compress random data sets by always more than 50%, regardless of th... | habedi/stack-exchange-dataset |
44,605 | Heuristic function | <p>Is there any way to prove that an admissible heuristic may not be consistent?
Most proof I came across are through examples .Is there a generalized proof?</p>
 | search algorithms artificial intelligence heuristics | 1 | Heuristic function -- (search algorithms artificial intelligence heuristics)
<p>Is there any way to prove that an admissible heuristic may not be consistent?
Most proof I came across are through examples .Is there a generalized proof?</p>
 | habedi/stack-exchange-dataset |
44,610 | How does the Sutherland-Hodgman Algorithm work? | <p>The following are the <a href="https://i.imgur.com/FNZnoyn.jpg?1" rel="nofollow noreferrer">Pages-96</a> and <a href="https://i.imgur.com/ASDTQ33.jpg?1" rel="nofollow noreferrer">Page-97</a> of the book Schaum's outline series of Computer Graphics.</p>

<p>The algorithm considers several things:</p>

... | graphics | 1 | How does the Sutherland-Hodgman Algorithm work? -- (graphics)
<p>The following are the <a href="https://i.imgur.com/FNZnoyn.jpg?1" rel="nofollow noreferrer">Pages-96</a> and <a href="https://i.imgur.com/ASDTQ33.jpg?1" rel="nofollow noreferrer">Page-97</a> of the book Schaum's outline series of Computer Graphics.</p>&#x... | habedi/stack-exchange-dataset |
44,623 | How to compare the time-complexity of an optimized algorithm with that of the original? | <p>I had an algorithm with time-complexity of $O(h\times w)$, knowing $h$ is the height and $w$ is the width of an image being processed (or a simple matrix of size $h\times w$).</p>

<p>I managed to reduce the range that the algorithm process. So rather than dealing with $h\times w$ elements, it is dealing wit... | algorithm analysis time complexity asymptotics runtime analysis performance | 1 | How to compare the time-complexity of an optimized algorithm with that of the original? -- (algorithm analysis time complexity asymptotics runtime analysis performance)
<p>I had an algorithm with time-complexity of $O(h\times w)$, knowing $h$ is the height and $w$ is the width of an image being processed (or a simple m... | habedi/stack-exchange-dataset |
44,629 | Why computer science papers rarely use advanced mathematics? | <p>I am a M.Sc. student in computer science, working on information networks and recommender systems. This days when I went through the top-tier conferences papers in the field I have seen most of them use solely simple machine learning tools such as generalized linear model, Expectation Maximization, Maximum Likelihoo... | research | 1 | Why computer science papers rarely use advanced mathematics? -- (research)
<p>I am a M.Sc. student in computer science, working on information networks and recommender systems. This days when I went through the top-tier conferences papers in the field I have seen most of them use solely simple machine learning tools su... | habedi/stack-exchange-dataset |
44,633 | Which matrix of Q values is being used here? | <p>This question refers to this paper: <a href="http://www.cs.toronto.edu/~fritz/absps/nips00-bs.pdf" rel="nofollow">Using Free Energies to Represent Q-values in a Multiagent Reinforcement Learning Task</a></p>

<p>In section 2.1, equations (5) and (6), I am wondering which Q values are being used to adjust the... | dynamic programming approximation neural networks | 1 | Which matrix of Q values is being used here? -- (dynamic programming approximation neural networks)
<p>This question refers to this paper: <a href="http://www.cs.toronto.edu/~fritz/absps/nips00-bs.pdf" rel="nofollow">Using Free Energies to Represent Q-values in a Multiagent Reinforcement Learning Task</a></p>

... | habedi/stack-exchange-dataset |
44,638 | What is a Universal Turing machine? | <p>Could a Universal Turing machine be set up so that it is able to 'reprogram' itself to 'behave' like any specific Turing machine without using some 'outside' source of info to cause it to do this?</p>
 | computability turing machines recursion theory | 1 | What is a Universal Turing machine? -- (computability turing machines recursion theory)
<p>Could a Universal Turing machine be set up so that it is able to 'reprogram' itself to 'behave' like any specific Turing machine without using some 'outside' source of info to cause it to do this?</p>
 | habedi/stack-exchange-dataset |
44,649 | pseudo clique with at least connectivity x and maximum weight of the nodes | <p>Let $G=(N,E)$ be a undirected graph of nodes $N$ and edges $E$. Each node $n \in N$ has a weight $w(n)$. The weight of a graph is defined as the sum of the weights of its nodes, i.e., by $w(G) = \sum_{n \in N}w(n)$. The connectivity of the graph is defined to be $c(G) = \#E_G / (\#N_G \cdot (\#N_G - 1)/2)$ -- this... | algorithms graphs clique | 1 | pseudo clique with at least connectivity x and maximum weight of the nodes -- (algorithms graphs clique)
<p>Let $G=(N,E)$ be a undirected graph of nodes $N$ and edges $E$. Each node $n \in N$ has a weight $w(n)$. The weight of a graph is defined as the sum of the weights of its nodes, i.e., by $w(G) = \sum_{n \in N}w(n... | habedi/stack-exchange-dataset |
44,656 | In an Inverted Page Table, will following chains happen very often for small addresses? | <p>I just learned about the Inverted Page Table and immediately thought about the chaining model used. 
If two processes use the same virtual address, resolving the address will have to include following the chaining information in the table.</p>

<p>If all memory addresses were used uniformly, that should ... | performance virtual memory paging | 1 | In an Inverted Page Table, will following chains happen very often for small addresses? -- (performance virtual memory paging)
<p>I just learned about the Inverted Page Table and immediately thought about the chaining model used. 
If two processes use the same virtual address, resolving the address will have to inc... | habedi/stack-exchange-dataset |
44,665 | Why don't 2 GPUs double the graphics performance of a computer compared to a single GPU? | <p>Obviously, if you have 2 GPUs, it is double the hardware, and thus it should be double the power of a single GPU (assuming all GPUs are the same, of course). So why is this not the case? I searched this question on Google and things about optimization and things came up, but I still don't understand.</p>
 | computer architecture parallel computing efficiency | 1 | Why don't 2 GPUs double the graphics performance of a computer compared to a single GPU? -- (computer architecture parallel computing efficiency)
<p>Obviously, if you have 2 GPUs, it is double the hardware, and thus it should be double the power of a single GPU (assuming all GPUs are the same, of course). So why is thi... | habedi/stack-exchange-dataset |
44,670 | minimum subset of dominating 2D points | <p>From an initial set $S$ of 2D points, how to efficiently compute a minimum(-size) dominating subset $M$ ?</p>

<p>$M$ is a dominating subset of $S$ if for any $(x,y)$ in $S$ there is at least one point (a,b) in M such that $x \le a$ and $y \le b$</p>

<p>Another related question: is any minimal set a... | algorithms data structures time complexity sorting | 1 | minimum subset of dominating 2D points -- (algorithms data structures time complexity sorting)
<p>From an initial set $S$ of 2D points, how to efficiently compute a minimum(-size) dominating subset $M$ ?</p>

<p>$M$ is a dominating subset of $S$ if for any $(x,y)$ in $S$ there is at least one point (a,b) in M s... | habedi/stack-exchange-dataset |
44,679 | Merge two series of sorted number, one much longer than the other | <p>This is the problem:</p>

<blockquote>
 <p>Merge two sorted series of numbers. Their lengths are $n$ and $m$, respectively, but $n \gg m$. Your algoritm should take $O(m \log(n/m))$
 comparisons. </p>
</blockquote>

<p>I have come up with this algorithm:</p>

<pre><code>1. Choo... | algorithms algorithm analysis runtime analysis sorting | 1 | Merge two series of sorted number, one much longer than the other -- (algorithms algorithm analysis runtime analysis sorting)
<p>This is the problem:</p>

<blockquote>
 <p>Merge two sorted series of numbers. Their lengths are $n$ and $m$, respectively, but $n \gg m$. Your algoritm should take $O(m \log(n/m... | habedi/stack-exchange-dataset |
44,680 | Merging of two convex polygon chains in O(log n) | <p>Assume I have a polygon chain implementation which is backed by a key-value store which stores the position of a point inside the chain as key and the point itself as value. So a polygon chain of the points $p_1\rightarrow p_2\rightarrow p_3$ is stored as $\{0\Rightarrow p_1,1\Rightarrow p_2,2\Rightarrow p_3\}$. The... | data structures time complexity computational geometry | 1 | Merging of two convex polygon chains in O(log n) -- (data structures time complexity computational geometry)
<p>Assume I have a polygon chain implementation which is backed by a key-value store which stores the position of a point inside the chain as key and the point itself as value. So a polygon chain of the points $... | habedi/stack-exchange-dataset |
44,690 | How can an approximation ratio be less than 1? | <p>A question in my algorithms text-book requires that we,</p>

<blockquote>
 <p>Describe an efficient $(1 - \frac{1}{k})$ -approximation algorithm for this
 problem.</p>
</blockquote>

<p>It is my understanding that $(1 - \frac{1}{k})$ being $p(n)$ is the approximation ratio and that an a... | algorithms terminology approximation | 1 | How can an approximation ratio be less than 1? -- (algorithms terminology approximation)
<p>A question in my algorithms text-book requires that we,</p>

<blockquote>
 <p>Describe an efficient $(1 - \frac{1}{k})$ -approximation algorithm for this
 problem.</p>
</blockquote>

<p>It is my und... | habedi/stack-exchange-dataset |
44,695 | Finding common edges of two graphs | <p>Is there any algorithm that finds the common edges and vertices between two graphs? Its not a common subgraph problem though, the edges which are common between the two graphs may not be connected to each other, may be far apart. How to find all the common edges in the graph? Like finding the common subgraphs betwee... | graphs | 1 | Finding common edges of two graphs -- (graphs)
<p>Is there any algorithm that finds the common edges and vertices between two graphs? Its not a common subgraph problem though, the edges which are common between the two graphs may not be connected to each other, may be far apart. How to find all the common edges in the ... | habedi/stack-exchange-dataset |
44,700 | Minimal size of a context-free grammar which defines $L_n=\{a^k\mid 1\le k\le n\}$ | <p>I am looking for the minimal size of a context-free grammar which defines the finite language $$L_n=\{a^k\mid 1\le k\le n\}.$$
The size of a grammar is defined as the total length of all right-hand sides of the rules.<br>
For example a grammar with
$$S\to A_1A_1\\A_1\to A_2A_2\\A_2\to A_3A_3\\A_3\to A_4A... | formal languages context free formal grammars data compression | 1 | Minimal size of a context-free grammar which defines $L_n=\{a^k\mid 1\le k\le n\}$ -- (formal languages context free formal grammars data compression)
<p>I am looking for the minimal size of a context-free grammar which defines the finite language $$L_n=\{a^k\mid 1\le k\le n\}.$$
The size of a grammar is defined as... | habedi/stack-exchange-dataset |
44,705 | Linear programming with absolute values | <p>I know that sometimes we can use absolute values into the objective functions or constraints. Is it always possible to use them, anywhere ?</p>

<p>Example of use of absolute values:</p>

<pre><code>Minimize |a+b+c| + |a-c| s.t.
 |a| + b > 3
 | |a| - |b| | <= 5 
 | |b| - 3 | = 0
... | linear programming integer programming | 1 | Linear programming with absolute values -- (linear programming integer programming)
<p>I know that sometimes we can use absolute values into the objective functions or constraints. Is it always possible to use them, anywhere ?</p>

<p>Example of use of absolute values:</p>

<pre><code>Minimize |a+b+c| +... | habedi/stack-exchange-dataset |
44,710 | Please explain a greedy algorithm in a naive manner | <p>I am a beginner in the topic of algorithms. I have a query about Greedy Algorithms.</p>

<p>From what I understand, if there is a function and we are supposed to find its maxima/minima, if we find the local maxima/minima, we become 'greedy' and declare that as the global maxima/minima.</p>

<p>I supp... | algorithms terminology greedy algorithms | 1 | Please explain a greedy algorithm in a naive manner -- (algorithms terminology greedy algorithms)
<p>I am a beginner in the topic of algorithms. I have a query about Greedy Algorithms.</p>

<p>From what I understand, if there is a function and we are supposed to find its maxima/minima, if we find the local maxi... | habedi/stack-exchange-dataset |
44,717 | Simplest Turing-complete ruleset for Markov algorithm | <p>Is there an example of a <em>particular ruleset</em> for a <a href="https://en.wikipedia.org/wiki/Markov_algorithm">Markov algorithm</a> that is <a href="https://en.wikipedia.org/wiki/Turing_completeness">Turing-complete</a>? If so, what is the simplest example of such a ruleset?</p>
 | computability turing machines computation models turing completeness term rewriting | 1 | Simplest Turing-complete ruleset for Markov algorithm -- (computability turing machines computation models turing completeness term rewriting)
<p>Is there an example of a <em>particular ruleset</em> for a <a href="https://en.wikipedia.org/wiki/Markov_algorithm">Markov algorithm</a> that is <a href="https://en.wikipedia... | habedi/stack-exchange-dataset |
44,718 | Bias of first values produced by a family of RNGs | <p>Suppose I'm doing a large number of <strong>pseudo-random but deterministic</strong> experiments, where each experiment requires generating several random numbers.</p>

<p>I'm approaching this by having each experiment use a <strong>random number generator seeded with a random-looking seed</strong> - e.g. ha... | randomness pseudo random generators | 1 | Bias of first values produced by a family of RNGs -- (randomness pseudo random generators)
<p>Suppose I'm doing a large number of <strong>pseudo-random but deterministic</strong> experiments, where each experiment requires generating several random numbers.</p>

<p>I'm approaching this by having each experiment... | habedi/stack-exchange-dataset |
44,733 | Model paths by regular languages | <p>I want use DFA to describe a sequence of movements in a 2D-space (language will be the path accepted by automaton in a particular case).</p>

<p>That is a typical modeling problem: how can I encode a sequence of 2D movements in a DFA?</p>

<p>Infact, walking through DFA or NFA seems a process analog... | formal languages regular languages automata finite automata computation models | 1 | Model paths by regular languages -- (formal languages regular languages automata finite automata computation models)
<p>I want use DFA to describe a sequence of movements in a 2D-space (language will be the path accepted by automaton in a particular case).</p>

<p>That is a typical modeling problem: how can I ... | habedi/stack-exchange-dataset |
44,734 | Can you increase data rate by increasing number of bits? | <p>My question is on data rate and baud rate.</p>

<p>data rate = baud rate * n</p>

<p>The question is, can you keep on increasing the data rate by increasing baud rate or number of bits.</p>

<p>I believe it can be increased by increasing the baud rate but what about the latter part? </p>
 | data structures | 1 | Can you increase data rate by increasing number of bits? -- (data structures)
<p>My question is on data rate and baud rate.</p>

<p>data rate = baud rate * n</p>

<p>The question is, can you keep on increasing the data rate by increasing baud rate or number of bits.</p>

<p>I believe it can be i... | habedi/stack-exchange-dataset |
44,740 | What is the best complexity of finding a minimum in a matrix? | <p>Given a matrix $\mathsf{a}$ of size $K\times N$, what is the best complexity of finding the minimum value?</p>

<p>Here is a pseudo code:</p>

<pre><code>function find_min(a)
 imin, jmin = 1, 1
 for k = 1 to K
 for n = 1 to N
 if a[k, n] < a[imin, jmin]
... | algorithms time complexity asymptotics | 1 | What is the best complexity of finding a minimum in a matrix? -- (algorithms time complexity asymptotics)
<p>Given a matrix $\mathsf{a}$ of size $K\times N$, what is the best complexity of finding the minimum value?</p>

<p>Here is a pseudo code:</p>

<pre><code>function find_min(a)
 imin, jmin =... | habedi/stack-exchange-dataset |
44,748 | How do I tell if a comparison network sorts? | <p>I am presented with a comparison network. How can I determine if the comparison network is a sorting network? In the image below there is an example of a selection sort and insertion sort network. The intent is to have a comparison network and sort numeric values. If I test 2^n values in this case 2^8. This is a lot... | sorting | 1 | How do I tell if a comparison network sorts? -- (sorting)
<p>I am presented with a comparison network. How can I determine if the comparison network is a sorting network? In the image below there is an example of a selection sort and insertion sort network. The intent is to have a comparison network and sort numeric va... | habedi/stack-exchange-dataset |
44,749 | Which all nodes will qualify as an ancestor? | <p>I was going through the fundamentals of tree structure and the definition for <em>ancestor</em> is as follows:</p>

<blockquote>
 <p>A node u is an ancestor of v if there is a path from u to v.</p>
</blockquote>

<p><a href="https://i.stack.imgur.com/VAG9p.png" rel="nofollow noreferrer"><img... | terminology data structures trees | 1 | Which all nodes will qualify as an ancestor? -- (terminology data structures trees)
<p>I was going through the fundamentals of tree structure and the definition for <em>ancestor</em> is as follows:</p>

<blockquote>
 <p>A node u is an ancestor of v if there is a path from u to v.</p>
</blockquote>
... | habedi/stack-exchange-dataset |
44,758 | Dynamic Programming Travel Planning Problem | <p>You want to visit n cities: $0 → 1 → 2 → · · · → n$. </p>

<p>For traveling between city $i$ and $i + 1$ $(0 ≤ i < n) $ you need to choose between two modes of transportation: train or plane. You are starting at the train station of city $0$ and want to end up at the airport of city $n$. </p>

<p>... | algorithms dynamic programming | 1 | Dynamic Programming Travel Planning Problem -- (algorithms dynamic programming)
<p>You want to visit n cities: $0 → 1 → 2 → · · · → n$. </p>

<p>For traveling between city $i$ and $i + 1$ $(0 ≤ i < n) $ you need to choose between two modes of transportation: train or plane. You are starting at the train stat... | habedi/stack-exchange-dataset |
44,763 | Could the Halting Problem be "resolved" by escaping to a higher-level description of computation? | <p>I've recently heard an interesting analogy which states that Turing's proof of the undecidability of the halting problem is very similar to Russell's barber paradox.</p>

<p>So I got to wonder: mathematicians did eventually manage to make set theory consistent by transitioning from Cantor's naive formulation... | computability turing machines computation models halting problem | 1 | Could the Halting Problem be "resolved" by escaping to a higher-level description of computation? -- (computability turing machines computation models halting problem)
<p>I've recently heard an interesting analogy which states that Turing's proof of the undecidability of the halting problem is very similar to Russell's... | habedi/stack-exchange-dataset |
44,770 | Complexity of cubic graph decomposition | <p>I am aware that deciding the existence of decomposition of a cubic graph into edge-disjoint claws is polynomial time solvable. Since a cubic graph has a decomposition into edge-disjoint claws if and only if it is bipartite.</p>

<blockquote>
 <p>What is the complexity of deciding the existence of decomp... | complexity theory graphs | 1 | Complexity of cubic graph decomposition -- (complexity theory graphs)
<p>I am aware that deciding the existence of decomposition of a cubic graph into edge-disjoint claws is polynomial time solvable. Since a cubic graph has a decomposition into edge-disjoint claws if and only if it is bipartite.</p>

<blockquot... | habedi/stack-exchange-dataset |
44,776 | Is the front-side bus multiplier the same as how many transfers it does per second? | <h3>What I am doing:</h3>

<p>I've been reading <a href="https://communities.intel.com/message/46993" rel="nofollow">there</a> about front-side busses (FSB) and their cycles per second (MHz) vs. bandwidth (Millions of Transactions per second or MT/s).</p>

<h3>What I've understood:</h3>

<p>FSB'... | computer architecture | 1 | Is the front-side bus multiplier the same as how many transfers it does per second? -- (computer architecture)
<h3>What I am doing:</h3>

<p>I've been reading <a href="https://communities.intel.com/message/46993" rel="nofollow">there</a> about front-side busses (FSB) and their cycles per second (MHz) vs. bandwi... | habedi/stack-exchange-dataset |
44,779 | Good mathematical book on algorithms | <p>I’m a sucker for mathematical elegance and rigour, and now am looking for such literature on algorithms and algorithm analysis. Now, it doesn’t matter much to me <em>what</em> algorithms are covered, but very much <em>how</em> they are presented and treated.¹ I most value a very clear and precise language which <em>... | algorithms algorithm analysis reference request books | 1 | Good mathematical book on algorithms -- (algorithms algorithm analysis reference request books)
<p>I’m a sucker for mathematical elegance and rigour, and now am looking for such literature on algorithms and algorithm analysis. Now, it doesn’t matter much to me <em>what</em> algorithms are covered, but very much <em>how... | habedi/stack-exchange-dataset |
44,780 | Showing that the set of DTMs that run forever is not Turing-recognizable | <p>The language A, that is all DTMS that run forever on input. </p>

<p>Would this not just be the HALT problem?</p>

<p>Therefore no reduction or proof is necessary, other then stating that?</p>

<p>ANSWER FOUND:
I think i have it, if it was Turing Recognizable, then it would be possible to... | computability turing machines halting problem semi decidability | 1 | Showing that the set of DTMs that run forever is not Turing-recognizable -- (computability turing machines halting problem semi decidability)
<p>The language A, that is all DTMS that run forever on input. </p>

<p>Would this not just be the HALT problem?</p>

<p>Therefore no reduction or proof is necess... | habedi/stack-exchange-dataset |
44,782 | Showing NP-hardness by reducing from a search problem | <p>I'm comfortable with showing NP-completeness of a decision problem: just take some problem that is known to be hard and reduce it to your new problem. This establishes NP-hardness of the new problem.</p>

<p>But we can also have NP-hard search problems. For example, it is claimed in the introduction of <a hr... | reductions np hard search problem | 1 | Showing NP-hardness by reducing from a search problem -- (reductions np hard search problem)
<p>I'm comfortable with showing NP-completeness of a decision problem: just take some problem that is known to be hard and reduce it to your new problem. This establishes NP-hardness of the new problem.</p>

<p>But we c... | habedi/stack-exchange-dataset |
44,786 | From context-free to context-sensitive | <p>I have a context-free language $L(G)$. I'm reading in a <a href="https://books.google.it/books?id=c42oYf4zBzMC&lpg=PA476&ots=frwFUzt-55&dq=prove%20that%20the%20intersection%20of%20a%20context%20sensitive%20language%20is%20empty%20is%20undecidable&pg=PA476#v=onepage&q&f=false" rel="nofollow">b... | formal languages context free context sensitive | 1 | From context-free to context-sensitive -- (formal languages context free context sensitive)
<p>I have a context-free language $L(G)$. I'm reading in a <a href="https://books.google.it/books?id=c42oYf4zBzMC&lpg=PA476&ots=frwFUzt-55&dq=prove%20that%20the%20intersection%20of%20a%20context%20sensitive%20languag... | habedi/stack-exchange-dataset |
44,791 | Devising an Algorithm for Linear Combination with Column Restrictions | <p><strong>Application:</strong></p>

<p>We intend to factor an integer $N$ using a variation of the <a href="http://en.wikipedia.org/wiki/Rational_sieve" rel="nofollow noreferrer">rational sieve</a>.</p>

<p>This involves constructing a congruence of squares modulo $N$ from a set of linear relations $$... | algorithms time complexity number theory linear algebra factoring | 1 | Devising an Algorithm for Linear Combination with Column Restrictions -- (algorithms time complexity number theory linear algebra factoring)
<p><strong>Application:</strong></p>

<p>We intend to factor an integer $N$ using a variation of the <a href="http://en.wikipedia.org/wiki/Rational_sieve" rel="nofollow no... | habedi/stack-exchange-dataset |
44,798 | Inferring Social Ties | <p>In some papers, they proposed a model in which the joint posterior probability was modeled as[1]:
$$ P(Y|\textbf{X},G) = \frac{P(\textbf{X},G|Y)P(Y)}{P(X,G)} \propto P(\textbf{X}|Y) \cdot P(Y|G)$$
where $\textbf{X}$ is attribute vectors set and $Y$ is the labels of all the edges in the network. </p>

... | machine learning | 1 | Inferring Social Ties -- (machine learning)
<p>In some papers, they proposed a model in which the joint posterior probability was modeled as[1]:
$$ P(Y|\textbf{X},G) = \frac{P(\textbf{X},G|Y)P(Y)}{P(X,G)} \propto P(\textbf{X}|Y) \cdot P(Y|G)$$
where $\textbf{X}$ is attribute vectors set and $Y$ is the labels of... | habedi/stack-exchange-dataset |
44,805 | Is there any development in continuous-value computers? | <p>Is there anything that hints at the possibility of a (modern) continuous-value computer, since modern computers are based on discrete arithmetic?</p>

<p>I guess the old analog computers were of this continuous-value type, but is there any modern development?</p>

<p>Do you know something about the i... | computer architecture | 1 | Is there any development in continuous-value computers? -- (computer architecture)
<p>Is there anything that hints at the possibility of a (modern) continuous-value computer, since modern computers are based on discrete arithmetic?</p>

<p>I guess the old analog computers were of this continuous-value type, but... | habedi/stack-exchange-dataset |
44,810 | NP Complete Subset GCD Proof | <p>$SubsetGCD$ is described by the following:</p>

<p>instance: A set of positive integers $S$ and an integer $k$ <BR>
question: does there exist a subset $S'$ of $S$ of size $k$ such that $GCD(S') = GCD(S)$ </p>

<p>Prove that $SubsetGCD$ is np complete.</p>

<p>The hint for the problem is ... | np complete reductions decision problem np | 1 | NP Complete Subset GCD Proof -- (np complete reductions decision problem np)
<p>$SubsetGCD$ is described by the following:</p>

<p>instance: A set of positive integers $S$ and an integer $k$ <BR>
question: does there exist a subset $S'$ of $S$ of size $k$ such that $GCD(S') = GCD(S)$ </p>

<p>Prove ... | habedi/stack-exchange-dataset |
44,820 | What does pre-, post- and in-order walk mean for a n-ary tree? | <p>The tree traversal methods explained in this <a href="https://en.wikipedia.org/wiki/Tree_traversal" rel="noreferrer">Wikipedia article</a> are pre-order, post-order and in-order. Are these methods limited to binary trees? The algorithm seems to be defined in terms of left and right child. If it can be used for n-ary... | graphs trees graph traversal | 1 | What does pre-, post- and in-order walk mean for a n-ary tree? -- (graphs trees graph traversal)
<p>The tree traversal methods explained in this <a href="https://en.wikipedia.org/wiki/Tree_traversal" rel="noreferrer">Wikipedia article</a> are pre-order, post-order and in-order. Are these methods limited to binary trees... | habedi/stack-exchange-dataset |
44,823 | Why is a quantum computer not capable of solving more problems than a classical computer? | <p>On the Wikipedia page for <a href="https://en.wikipedia.org/wiki/Quantum_algorithm">quantum algorithm</a> I read that</p>

<blockquote>
 <p>[a]ll problems which can be solved on a quantum computer can be solved on a classical computer. In particular, problems which are undecidable using classical comput... | computability computation models quantum computing simulation | 1 | Why is a quantum computer not capable of solving more problems than a classical computer? -- (computability computation models quantum computing simulation)
<p>On the Wikipedia page for <a href="https://en.wikipedia.org/wiki/Quantum_algorithm">quantum algorithm</a> I read that</p>

<blockquote>
 <p>[a]ll p... | habedi/stack-exchange-dataset |
44,828 | Bringing images into alignment | <p>I observe a scene with two cameras, c1 and c2, that produce two images i1 and i2, respectively. What I now want is to bring i1 and i2 into alignment, that is I want to know where pixel (x,y) in i1 is in i2. This "alignment-matrix" should be valid in general, that is not only for i1 and i2, but also for further image... | computational geometry image processing computer vision | 1 | Bringing images into alignment -- (computational geometry image processing computer vision)
<p>I observe a scene with two cameras, c1 and c2, that produce two images i1 and i2, respectively. What I now want is to bring i1 and i2 into alignment, that is I want to know where pixel (x,y) in i1 is in i2. This "alignment-ma... | habedi/stack-exchange-dataset |
44,838 | Calibration and overlay of RGBD with a thermal camera | <p>I have a thermal camera that I would like to overlay automatically to the output of a RGBD camera (e.g., Kinect). </p>

<p>I can retrieve the intrinsic parameters of the thermal camera by using a special board I built, that allows the thermal camera to give as output a series of points similar to the ones o... | computer vision | 1 | Calibration and overlay of RGBD with a thermal camera -- (computer vision)
<p>I have a thermal camera that I would like to overlay automatically to the output of a RGBD camera (e.g., Kinect). </p>

<p>I can retrieve the intrinsic parameters of the thermal camera by using a special board I built, that allows th... | habedi/stack-exchange-dataset |
44,849 | Find variance within one pass | <p>Given a list of real numbers. Is it possible to find the variance with no more than 1 iteration with constant space complexity? </p>
 | algorithms arithmetic | 1 | Find variance within one pass -- (algorithms arithmetic)
<p>Given a list of real numbers. Is it possible to find the variance with no more than 1 iteration with constant space complexity? </p>
 | habedi/stack-exchange-dataset |
44,855 | If recursive Fibonacci is $O(2^N)$ then why do I get 15 calls for N=5? | <p>I learned that recursive Fibonacci is $O(2^N)$.</p>

<p>However, when I implement it and print out the recursive calls that were made, I only get 15 calls for N=5. What I am missing? Should it not be 32 or near abouts? It's like less then half!</p>

<pre><code>$COUNT = 0

def fibonacci( n )&#... | algorithm analysis asymptotics runtime analysis recursion | 1 | If recursive Fibonacci is $O(2^N)$ then why do I get 15 calls for N=5? -- (algorithm analysis asymptotics runtime analysis recursion)
<p>I learned that recursive Fibonacci is $O(2^N)$.</p>

<p>However, when I implement it and print out the recursive calls that were made, I only get 15 calls for N=5. What I am m... | habedi/stack-exchange-dataset |
44,860 | Fundamental and essential matrices, value of intrinsic parameters | <p>I observe a scene with two cameras, c1 and c2, that produce two images i1 and i2, respectively. What I ultimately want to do is to use information of image i1 and image2 simultaneously, e.g., for object detection.</p>

<p>As far as I understand it, I would not be required to find the intrinsic parameters of ... | computational geometry image processing computer vision | 1 | Fundamental and essential matrices, value of intrinsic parameters -- (computational geometry image processing computer vision)
<p>I observe a scene with two cameras, c1 and c2, that produce two images i1 and i2, respectively. What I ultimately want to do is to use information of image i1 and image2 simultaneously, e.g.... | habedi/stack-exchange-dataset |
44,862 | Getting the essential from the fundamental matrix | <p>Is it possible to get E from F? I suppose that can't work, because then I could calculate the the extrinsic (and maybe also intrinsic?) parameters of the cameras without a calibration object of known size etc. like so:</p>

<ol>
<li>Pick (8) corresponding points in images i1 and i2</li>
<li>Calculate... | computational geometry image processing computer vision | 1 | Getting the essential from the fundamental matrix -- (computational geometry image processing computer vision)
<p>Is it possible to get E from F? I suppose that can't work, because then I could calculate the the extrinsic (and maybe also intrinsic?) parameters of the cameras without a calibration object of known size e... | habedi/stack-exchange-dataset |
44,865 | What are algorithms for computing contours from given edges? | <p>Let's say I have a set of edges which makes the contour, however there are too many of them and some are too long. I have to remove edges, and shorten them to make contour. I <em>cannot</em> add new edges!</p>

<p>I am looking at least for the name of the algorithm to further look how this problem is solved.... | algorithms computational geometry | 1 | What are algorithms for computing contours from given edges? -- (algorithms computational geometry)
<p>Let's say I have a set of edges which makes the contour, however there are too many of them and some are too long. I have to remove edges, and shorten them to make contour. I <em>cannot</em> add new edges!</p>
&#x... | habedi/stack-exchange-dataset |
44,868 | Is there a more efficient algorithm than backtracking/dynamic programming? | <p>Consider the following game:</p>

<p>One day a castle is attacked at sunrise (by surprise) by n soldiers.</p>

<p>Each soldier carries a canon and a rifle. </p>

<p>The castle has strength s.</p>

<p>On the first day each soldier shoots his canon at the castle costing the castle n str... | algorithms algorithm analysis search algorithms dynamic programming backtracking | 1 | Is there a more efficient algorithm than backtracking/dynamic programming? -- (algorithms algorithm analysis search algorithms dynamic programming backtracking)
<p>Consider the following game:</p>

<p>One day a castle is attacked at sunrise (by surprise) by n soldiers.</p>

<p>Each soldier carries a can... | habedi/stack-exchange-dataset |
44,869 | What are the simplest examples of programs that we do not know whether they terminate? | <p>The halting problem states there is no algorithm that will determine if a given program halts. As a consequence, there should be programs about which we can not tell whether they terminate or not. What are the simplest (smallest) known examples of such programs?</p>
 | computability turing machines halting problem | 1 | What are the simplest examples of programs that we do not know whether they terminate? -- (computability turing machines halting problem)
<p>The halting problem states there is no algorithm that will determine if a given program halts. As a consequence, there should be programs about which we can not tell whether they ... | habedi/stack-exchange-dataset |
44,879 | Do Approximation Algorithms Analyzed in the Worst Case? | <p>From wikipedia:</p>
<blockquote>
<p>For some approximation algorithms it is possible to prove certain properties about the approximation of the optimum result. For example, a <span class="math-container">$ρ$</span>-approximation algorithm <span class="math-container">$A$</span> is defined to be an algorithm ... | algorithm analysis approximation | 1 | Do Approximation Algorithms Analyzed in the Worst Case? -- (algorithm analysis approximation)
<p>From wikipedia:</p>
<blockquote>
<p>For some approximation algorithms it is possible to prove certain properties about the approximation of the optimum result. For example, a <span class="math-container">$ρ$</span>-... | habedi/stack-exchange-dataset |
44,889 | Can an Earley Parser be made into a fuzzy parser similar to the Levenshtein Automata Algo for DFA? | <p>There's a way to perform fuzzy parsing (accepts strings even with typos to a certain edit distance), with a DFA and a run-time constructed Levenshtein Automata of the input word. Can something similar be done with an Earley parser? I'm finding it hard to understand the algorithm, let alone answer this question.</p... | algorithms context free finite automata parsers string metrics | 1 | Can an Earley Parser be made into a fuzzy parser similar to the Levenshtein Automata Algo for DFA? -- (algorithms context free finite automata parsers string metrics)
<p>There's a way to perform fuzzy parsing (accepts strings even with typos to a certain edit distance), with a DFA and a run-time constructed Levenshtein... | habedi/stack-exchange-dataset |
44,891 | "Most Similar Vector Problem" on an Integer Lattice | <p>I am currently working on problem that I think could be expressed as an integer lattice problem, and hoping to find some guidance on this forum.</p>

<p>Given $u \in \mathbb{R}^n$ and a <em>bounded</em> integer lattice $L = \mathbb{Z}^n \cap [-M,M]^n$, I would like to find an integer vector $v \in L$ such th... | reference request cryptography integers lattices | 1 | "Most Similar Vector Problem" on an Integer Lattice -- (reference request cryptography integers lattices)
<p>I am currently working on problem that I think could be expressed as an integer lattice problem, and hoping to find some guidance on this forum.</p>

<p>Given $u \in \mathbb{R}^n$ and a <em>bounded</em> ... | habedi/stack-exchange-dataset |
44,895 | How to read BNF syntax of C? | <p>Today I heard of <a href="https://en.wikipedia.org/wiki/Backus%E2%80%93Naur_Form" rel="nofollow">BNF</a> which is a language for languages. Also heard that it specifies the entire syntax of C in four pages. So I thought of checking it out. After reading through <a href="http://www.cs.man.ac.uk/~pjj/bnf/bnf.html" rel... | context free formal grammars programming languages syntax | 1 | How to read BNF syntax of C? -- (context free formal grammars programming languages syntax)
<p>Today I heard of <a href="https://en.wikipedia.org/wiki/Backus%E2%80%93Naur_Form" rel="nofollow">BNF</a> which is a language for languages. Also heard that it specifies the entire syntax of C in four pages. So I thought of ch... | habedi/stack-exchange-dataset |
44,899 | Are there other interpretations of |G| than |V|, that is |V(G)|? | <p>This may be a basic question, but I'm hoping someone can settle this nagging doubt I'm having. I'm reading up on FPT complexity using a book by Downey and Fellows. It has some introductory examples which detail complexity in terms of $|G|$, which seems to denote $|V|$ as mentioned <a href="https://math.stackexchange... | complexity theory graphs | 1 | Are there other interpretations of |G| than |V|, that is |V(G)|? -- (complexity theory graphs)
<p>This may be a basic question, but I'm hoping someone can settle this nagging doubt I'm having. I'm reading up on FPT complexity using a book by Downey and Fellows. It has some introductory examples which detail complexity ... | habedi/stack-exchange-dataset |
44,907 | Kleene star operation on the empty language | <p>In my text book it is mentioned that: $\emptyset^*=\{\epsilon\}$ where $\emptyset$ is an empty language.</p>

<p>However, we know that $L \cdot \emptyset = \emptyset$, where $L$ is any Language.</p>

<p>I am not able to intuitively grasp this concept because the Kleene star operation points towards t... | formal languages kleene star | 1 | Kleene star operation on the empty language -- (formal languages kleene star)
<p>In my text book it is mentioned that: $\emptyset^*=\{\epsilon\}$ where $\emptyset$ is an empty language.</p>

<p>However, we know that $L \cdot \emptyset = \emptyset$, where $L$ is any Language.</p>

<p>I am not able to int... | habedi/stack-exchange-dataset |
44,915 | Data General MV/8000 virtues of "No mode bit" | <p>I'm reading Tracy Kidder's "The Soul of a New Machine" where a team at Data General design a new machine (codenamed "Eagle", later named MV/8000). It is 32-bit extension of a previous architecture (the 16-bit Eclipse). One of the revolving themes seems to be, that they don't want to create a machine with a mode bit ... | computer architecture | 1 | Data General MV/8000 virtues of "No mode bit" -- (computer architecture)
<p>I'm reading Tracy Kidder's "The Soul of a New Machine" where a team at Data General design a new machine (codenamed "Eagle", later named MV/8000). It is 32-bit extension of a previous architecture (the 16-bit Eclipse). One of the revolving them... | habedi/stack-exchange-dataset |
44,924 | Why is pure literal elimination absent in DPLL-based algorithms like Chaff? | <p>I'm looking into various <a href="http://web.stanford.edu/class/cs357/lectures/sat.pdf" rel="nofollow">SAT-solvers</a> and trying to understand how they work and why they are designed in certain ways. (But I'm not in a university at the moment and I do not know anyone who is a professor. So I'm posting here hoping t... | algorithms sat solvers | 1 | Why is pure literal elimination absent in DPLL-based algorithms like Chaff? -- (algorithms sat solvers)
<p>I'm looking into various <a href="http://web.stanford.edu/class/cs357/lectures/sat.pdf" rel="nofollow">SAT-solvers</a> and trying to understand how they work and why they are designed in certain ways. (But I'm not... | habedi/stack-exchange-dataset |
44,927 | How to exclude all points adjacent to a given point from the feasible region of IP | <p>Consider a basic integer program such as:</p>

<p>$$\begin{align} 
\min_x & \quad c^Tx \\
\text{s.t.} & \quad Ax \leq b \\
&\quad x_i \in \{-100,\ldots,100\}
\end{align}
$$</p>

<p>where $x \in \mathbb{Z}^n, A \in \mathbb{R}^{m \times n}$ and $b \in \mathbb{R^m}$.</p>&... | optimization discrete mathematics integer programming | 1 | How to exclude all points adjacent to a given point from the feasible region of IP -- (optimization discrete mathematics integer programming)
<p>Consider a basic integer program such as:</p>

<p>$$\begin{align} 
\min_x & \quad c^Tx \\
\text{s.t.} & \quad Ax \leq b \\
&\quad x_i \in \{-10... | habedi/stack-exchange-dataset |
44,933 | Solving a bivariate recurrence equation | <p>I'm dealing with this recurrence equation:</p>

<p>$\qquad\displaystyle T(m, n) = T(m/2, n/2) + T(m, n/2) + O(1)$.</p>

<p>Any idea how to solve this? I've looked in to few <a href="http://jeffe.cs.illinois.edu/teaching/algorithms/notes/99-recurrences.pdf" rel="nofollow">advanced resources</a> but th... | recurrence relation | 1 | Solving a bivariate recurrence equation -- (recurrence relation)
<p>I'm dealing with this recurrence equation:</p>

<p>$\qquad\displaystyle T(m, n) = T(m/2, n/2) + T(m, n/2) + O(1)$.</p>

<p>Any idea how to solve this? I've looked in to few <a href="http://jeffe.cs.illinois.edu/teaching/algorithms/notes... | habedi/stack-exchange-dataset |
44,942 | How to find a symmetric predecessor / successor | <p>Lets say we have a binary tree $T$ and we want to insert key $k$. Now, assuming $k\not\in T$, how do we find the symmetric predecessor/successor of $k$?</p>

<p>Does this relate to (pre/in/post)-order traversals in some way?</p>
 | data structures binary trees | 1 | How to find a symmetric predecessor / successor -- (data structures binary trees)
<p>Lets say we have a binary tree $T$ and we want to insert key $k$. Now, assuming $k\not\in T$, how do we find the symmetric predecessor/successor of $k$?</p>

<p>Does this relate to (pre/in/post)-order traversals in some way?</p... | habedi/stack-exchange-dataset |
44,944 | n log n = c. What are some good approximations of this? | <p>I am currently looking into Big O notation and computational complexity.</p>

<p>Problem 1.1 in CLRS asks what seems a basic question, which is to get an intuition about how different algorithmic complexities grow with the size of the input.</p>

<p>The question asks:</p>

<p><em>For each fun... | algorithms algorithm analysis asymptotics | 1 | n log n = c. What are some good approximations of this? -- (algorithms algorithm analysis asymptotics)
<p>I am currently looking into Big O notation and computational complexity.</p>

<p>Problem 1.1 in CLRS asks what seems a basic question, which is to get an intuition about how different algorithmic complexiti... | habedi/stack-exchange-dataset |
44,951 | Clique decision problem restricted to a subgraph | <p>I know that the clique problem is NP-complete. </p>

<p>However, what if we change the problem a little bit?</p>

<p>For example,</p>

<p>Given a graph $G(V,E)$, an integer $k$ and a subset $S$ of $m$ vertices, we are given a decision problem to find a clique with size $k$ contained within&nb... | complexity theory np complete decision problem | 1 | Clique decision problem restricted to a subgraph -- (complexity theory np complete decision problem)
<p>I know that the clique problem is NP-complete. </p>

<p>However, what if we change the problem a little bit?</p>

<p>For example,</p>

<p>Given a graph $G(V,E)$, an integer $k$ and a subset $S... | habedi/stack-exchange-dataset |
44,956 | Difference between $O(n^2)$ and $O(m)$ for algorithms on graphs | <p>Given a graph $G$ directed with n nodes and m edges, if an algorithm solves a problem $X$ on $G$ with a complexity $O(n^2)$, while an other algorithm solves same problem $X$ on $G$ but with complexity $O(m)$, what is the most efficient ?</p>
 | graphs algorithm analysis runtime analysis efficiency | 1 | Difference between $O(n^2)$ and $O(m)$ for algorithms on graphs -- (graphs algorithm analysis runtime analysis efficiency)
<p>Given a graph $G$ directed with n nodes and m edges, if an algorithm solves a problem $X$ on $G$ with a complexity $O(n^2)$, while an other algorithm solves same problem $X$ on $G$ but with com... | habedi/stack-exchange-dataset |
44,966 | Chomsky hierarchy type determined by language | <p>I have some modified automata and the task is to give the type of Chomsky hierarchy to it.
All task is between type 3 and 0 noninclusive.
For regular languages there are lot of tools and I can check it without problems, Turing Machine equivalent is also easy task, and there will be no such examples.</p>
... | automata proof techniques computation models | 1 | Chomsky hierarchy type determined by language -- (automata proof techniques computation models)
<p>I have some modified automata and the task is to give the type of Chomsky hierarchy to it.
All task is between type 3 and 0 noninclusive.
For regular languages there are lot of tools and I can check it without pro... | habedi/stack-exchange-dataset |
44,968 | About a step in the analysis of Quicksort by Sedgewick and Wayne | <p>In the book <em>Algorithms</em>, 4th Edition by Robert Sedgewick and Kevin Wayne, when they are analyzing quicksort (page 294), they present the sequence of transformations: 
$$\begin{gather*}
C_N = N + 1 + (C_0 + C_1 + \dots + C_{N-2} + C_{N-1})/N + (C_{N-1} + C_{N-2} + \dots + C_0)/N\\
NC_N = N(N+1) + ... | algorithm analysis asymptotics runtime analysis recurrence relation quicksort | 1 | About a step in the analysis of Quicksort by Sedgewick and Wayne -- (algorithm analysis asymptotics runtime analysis recurrence relation quicksort)
<p>In the book <em>Algorithms</em>, 4th Edition by Robert Sedgewick and Kevin Wayne, when they are analyzing quicksort (page 294), they present the sequence of transformati... | habedi/stack-exchange-dataset |
44,973 | Is $\epsilon$ always contained in $\Sigma^*$? | <p>Please correct me on any terminology. For some reason I'm a bit confused.</p>

<p>$\Sigma = \{\epsilon, 0, 1\}$</p>

<p>This means my alphabet, $\Sigma$, contains three symbols ($\epsilon, 0, 1$).</p>

<p>$\Sigma^*$ is the language over $\Sigma$, and it equals $\{\epsilon, 0, 1, 01, 10\}$.</p... | formal languages terminology regular languages | 1 | Is $\epsilon$ always contained in $\Sigma^*$? -- (formal languages terminology regular languages)
<p>Please correct me on any terminology. For some reason I'm a bit confused.</p>

<p>$\Sigma = \{\epsilon, 0, 1\}$</p>

<p>This means my alphabet, $\Sigma$, contains three symbols ($\epsilon, 0, 1$).</p>&#x... | habedi/stack-exchange-dataset |
44,981 | Least number of comparisons needed to sort (order) 5 elements | <p>Find the least number of comparisons needed to sort (order) five elements and
devise an algorithm that sorts these elements using this number of comparisons.</p>

<blockquote>
 <p><em><a href="http://www.math.mcgill.ca/olga/34006midsol.pdf">Solution</a>:</em> There are 5! = 120 possible outcomes. Th... | algorithms sorting lower bounds | 1 | Least number of comparisons needed to sort (order) 5 elements -- (algorithms sorting lower bounds)
<p>Find the least number of comparisons needed to sort (order) five elements and
devise an algorithm that sorts these elements using this number of comparisons.</p>

<blockquote>
 <p><em><a href="http://w... | habedi/stack-exchange-dataset |
44,983 | What is the relation between a regular language, $L$, and $\Sigma^*$? | <p>Let's say I have $\Sigma = \{0\}$.</p>

<p>Can a language $L$ be as large as $\Sigma^*$? So $L = \Sigma^*$.</p>

<p>Can a language $L$ be as small as just $\{0\}$? A subset of $\Sigma^*$.</p>

<p>Can multiple languages, $L_1, L_2$, come from the same $\Sigma$, i.e. be subsets of the same $\Si... | formal languages | 1 | What is the relation between a regular language, $L$, and $\Sigma^*$? -- (formal languages)
<p>Let's say I have $\Sigma = \{0\}$.</p>

<p>Can a language $L$ be as large as $\Sigma^*$? So $L = \Sigma^*$.</p>

<p>Can a language $L$ be as small as just $\{0\}$? A subset of $\Sigma^*$.</p>

<p>Can m... | habedi/stack-exchange-dataset |
44,997 | Finding similar high dimensional real vectors | <p>I have a collection of vectors $v_1,v_2\in [0,1]^n$ and I want to find similar pairs quickly. For similarity, I want to use the Euclidean distance metric $L: [0,1]^n \times [0,1]^n \longrightarrow R$. $n$ will be around $200$.</p>

<p>I've implemented Locality Similar Hashing (LSH) for word based documents, ... | hash cluster | 1 | Finding similar high dimensional real vectors -- (hash cluster)
<p>I have a collection of vectors $v_1,v_2\in [0,1]^n$ and I want to find similar pairs quickly. For similarity, I want to use the Euclidean distance metric $L: [0,1]^n \times [0,1]^n \longrightarrow R$. $n$ will be around $200$.</p>

<p>I've imple... | habedi/stack-exchange-dataset |
45,002 | Is HORN-SAT in LIN, if so why is that not an indication that P=LIN? | <p><a href="https://complexityzoo.uwaterloo.ca/Complexity_Zoo:L#LIN:_Linear_Time" rel="noreferrer">The Complexity Zoo</a> defines $LIN$ to be the class of decision problems solvable by a deterministic Turing machine in linear time.</p>

<p>$$LIN \subseteq P$$</p>

<p>Since HORN-SAT is solvable in $O(n)$... | complexity theory time complexity reductions | 1 | Is HORN-SAT in LIN, if so why is that not an indication that P=LIN? -- (complexity theory time complexity reductions)
<p><a href="https://complexityzoo.uwaterloo.ca/Complexity_Zoo:L#LIN:_Linear_Time" rel="noreferrer">The Complexity Zoo</a> defines $LIN$ to be the class of decision problems solvable by a deterministic T... | habedi/stack-exchange-dataset |
45,005 | Algorithm to check the distance between integers | <p>I have the next problem, and I was wondering whether it exists a way to solve it without having to iterate around all the array in the worst case.</p>

<p>I have a sorted array of pairwise distinct integers, say $[1,2,4,5,7,8]$
I need to know if there is a gap of at least two between two consecutive inte... | algorithms arrays | 1 | Algorithm to check the distance between integers -- (algorithms arrays)
<p>I have the next problem, and I was wondering whether it exists a way to solve it without having to iterate around all the array in the worst case.</p>

<p>I have a sorted array of pairwise distinct integers, say $[1,2,4,5,7,8]$
I nee... | habedi/stack-exchange-dataset |
45,007 | Why do reductions to NP-complete problems in NTIME(n) not break the nondeterministic time hierarchy? | <p>Let $\mathrm{L} \in \mathrm{NTIME}(n^3)$. Since $\mathrm{NTIME}(n^3) \subseteq \mathrm{NP}$, we have that $\mathrm{L} \le_p \mathrm{3SAT}$. However, $\mathrm{3SAT} \in \mathrm{NTIME}(n)$. Hence, $\mathrm{L} \in \mathrm{NTIME}(n)$. Thus, $\mathrm{NTIME}(n^3)\subseteq \mathrm{NTIME}(n)$ which implies the non-determini... | complexity theory reductions complexity classes | 1 | Why do reductions to NP-complete problems in NTIME(n) not break the nondeterministic time hierarchy? -- (complexity theory reductions complexity classes)
<p>Let $\mathrm{L} \in \mathrm{NTIME}(n^3)$. Since $\mathrm{NTIME}(n^3) \subseteq \mathrm{NP}$, we have that $\mathrm{L} \le_p \mathrm{3SAT}$. However, $\mathrm{3SAT}... | habedi/stack-exchange-dataset |
45,021 | Is there a computationally reasonable algorithm for generating a set of polygons from a set of 2d points? | <p>Is there a known/existing algorithm for taking a 2D canvas covered in arbitrarily/randomly distributed points and dividing it entirely into a set of non-overlapping polygons? An example of the kind of result I'm looking for:<a href="https://i.stack.imgur.com/OGCNl.png" rel="nofollow noreferrer"><img src="https://i.... | algorithms graphs | 1 | Is there a computationally reasonable algorithm for generating a set of polygons from a set of 2d points? -- (algorithms graphs)
<p>Is there a known/existing algorithm for taking a 2D canvas covered in arbitrarily/randomly distributed points and dividing it entirely into a set of non-overlapping polygons? An example o... | habedi/stack-exchange-dataset |
45,033 | Generating graphs such as found on Sedgewick's Algorithms book on the MST chapters | <p>I always wondered what the algorithm might be to generate graphs such as those found on Sedgewick's algorithms books (consider the picture on the left):</p>

<p><a href="https://i.stack.imgur.com/hE4dK.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/hE4dK.png" alt="enter image description ... | graphs sampling | 1 | Generating graphs such as found on Sedgewick's Algorithms book on the MST chapters -- (graphs sampling)
<p>I always wondered what the algorithm might be to generate graphs such as those found on Sedgewick's algorithms books (consider the picture on the left):</p>

<p><a href="https://i.stack.imgur.com/hE4dK.png... | habedi/stack-exchange-dataset |
45,038 | Is the superset and subset of a semi-decidable language also semi-decidable? | <p>Given three languages $L_1, L_2, L_3$ with $L_1$ and $L_3$ being semi-decidable and $L_1 \subseteq L_2, L_2 \subseteq L_3$. Can I deduce from these properties, that $L_2$ is also semi-decidable and how would I proof this?</p>

<p>Intuitionally it seems obvious that $L_2$ is also semi-decidable, but I didn't ... | semi decidability | 1 | Is the superset and subset of a semi-decidable language also semi-decidable? -- (semi decidability)
<p>Given three languages $L_1, L_2, L_3$ with $L_1$ and $L_3$ being semi-decidable and $L_1 \subseteq L_2, L_2 \subseteq L_3$. Can I deduce from these properties, that $L_2$ is also semi-decidable and how would I proof t... | habedi/stack-exchange-dataset |
45,045 | Converting final state PDA to empty stack PDA | <p>I'm having a problem understanding this conversion. Let's say we have a CFL like this:
$ { a^nb^m : n > m } $</p>

<p>A final state acceptance PDA for this language would push $A$ symbols in the stack for every 'a' input, and pop them for every 'b' input. If the stack has no more $A$s while we still h... | automata pushdown automata simulation | 1 | Converting final state PDA to empty stack PDA -- (automata pushdown automata simulation)
<p>I'm having a problem understanding this conversion. Let's say we have a CFL like this:
$ { a^nb^m : n > m } $</p>

<p>A final state acceptance PDA for this language would push $A$ symbols in the stack for every 'a... | habedi/stack-exchange-dataset |
45,056 | How to prove $0\neq1$ using the J rule? | <p>Suppose I have a simple dependent type theory with bottom, unit, sums, dependent pairs, dependent functions, natural numbers and homogeneous identity with J-elimination.</p>

<p>Is there a way to prove $(0 = 1) \rightarrow \bot$? Or do I need K for that?</p>
 | proof techniques type theory dependent types | 1 | How to prove $0\neq1$ using the J rule? -- (proof techniques type theory dependent types)
<p>Suppose I have a simple dependent type theory with bottom, unit, sums, dependent pairs, dependent functions, natural numbers and homogeneous identity with J-elimination.</p>

<p>Is there a way to prove $(0 = 1) \rightar... | habedi/stack-exchange-dataset |
45,061 | Definition and properties of support | <p>From <a href="http://www-users.cs.umn.edu/~kumar/papers/taper.pdf" rel="nofollow">Xiong, Hui, Shashi Shekhar, Pang-Ning Tan, and Vipin Kumar. “TAPER: A Two-Step Approach for All-Strong-Pairs Correlation Query in Large Databases.” Knowledge and Data Engineering, IEEE Transactions on 18, no. 4 (2006): 493–508.</a>
... | data mining statistics | 1 | Definition and properties of support -- (data mining statistics)
<p>From <a href="http://www-users.cs.umn.edu/~kumar/papers/taper.pdf" rel="nofollow">Xiong, Hui, Shashi Shekhar, Pang-Ning Tan, and Vipin Kumar. “TAPER: A Two-Step Approach for All-Strong-Pairs Correlation Query in Large Databases.” Knowledge and Data Eng... | habedi/stack-exchange-dataset |
45,067 | Approximate Bayesian Computation VS Monte Carlo Simulation | <p>I am a little confused about the differences between Approximation Bayesian Computation (ABC) and Monte Carlo Methods (MCM). Citing from wikipedia:</p>
<blockquote>
<p><strong>Approximate Bayesian computation</strong> (ABC) constitutes a class of computational methods rooted in Bayesian statistics. In all mo... | statistics monte carlo bayesian statistics | 1 | Approximate Bayesian Computation VS Monte Carlo Simulation -- (statistics monte carlo bayesian statistics)
<p>I am a little confused about the differences between Approximation Bayesian Computation (ABC) and Monte Carlo Methods (MCM). Citing from wikipedia:</p>
<blockquote>
<p><strong>Approximate Bayesian compu... | habedi/stack-exchange-dataset |
45,076 | "Compressing" rationals given error bounds | <p>I'm working on implementing some exact real arithmetic operations for fun. I've got the rough outline of how I want to do things as well and have figured out how to write most of the important algorithms (though I have not properly implemented them just yet).</p>

<p>Going against the "pre-mature optimizatio... | numerical analysis number formats | 1 | "Compressing" rationals given error bounds -- (numerical analysis number formats)
<p>I'm working on implementing some exact real arithmetic operations for fun. I've got the rough outline of how I want to do things as well and have figured out how to write most of the important algorithms (though I have not properly imp... | habedi/stack-exchange-dataset |
45,088 | Longest simple walk in a complete graph | <p>A <em>simple walk</em> is a path that does not contain the same edge twice. A simple walk can contain circuits and can be a circuit itself. It just shouldn't have the same edge twice.</p>

<p>A <em>simple undirected graph</em> is an undirected graph with no loops and multiple edges. A <em>complete graph</em>... | graphs | 1 | Longest simple walk in a complete graph -- (graphs)
<p>A <em>simple walk</em> is a path that does not contain the same edge twice. A simple walk can contain circuits and can be a circuit itself. It just shouldn't have the same edge twice.</p>

<p>A <em>simple undirected graph</em> is an undirected graph with no... | habedi/stack-exchange-dataset |
45,091 | Amortized analysis for doubling resizing array is ~3n | <p>I'm brushing up on stuff related to analysis of algorithms. And I have a question about <a href="http://www.cs.cmu.edu/afs/cs/academic/class/15451-s07/www/lecture_notes/lect0206.pdf" rel="nofollow noreferrer">this PDF I found</a>. This is where I'm confused:</p>
<blockquote>
<p>Question 2: What if instead we... | algorithm analysis mathematical analysis amortized analysis | 1 | Amortized analysis for doubling resizing array is ~3n -- (algorithm analysis mathematical analysis amortized analysis)
<p>I'm brushing up on stuff related to analysis of algorithms. And I have a question about <a href="http://www.cs.cmu.edu/afs/cs/academic/class/15451-s07/www/lecture_notes/lect0206.pdf" rel="nofollow n... | habedi/stack-exchange-dataset |
45,092 | Proof by Turing Reduction | <p>I need to proof the following by turing reduction.</p>

<p>Given two languages:</p>

<p>$Q= \{(\langle M_1 \rangle , \langle M_2 \rangle ) \mid L(M_1) = L(M_2)\}$</p>

<p>$I= \{\langle M \rangle \mid \;\vert L(M) \vert = \infty \}$</p>

<p>Where $\langle M_1 \rangle$ is the encoding o... | complexity theory turing machines reductions | 1 | Proof by Turing Reduction -- (complexity theory turing machines reductions)
<p>I need to proof the following by turing reduction.</p>

<p>Given two languages:</p>

<p>$Q= \{(\langle M_1 \rangle , \langle M_2 \rangle ) \mid L(M_1) = L(M_2)\}$</p>

<p>$I= \{\langle M \rangle \mid \;\vert L(M) \ver... | habedi/stack-exchange-dataset |
45,104 | How to turing reduce equivalent languages $Q$ to infinite language $I$ | <p>Given two languages:</p>

<p>$Q= \{(\langle M_1 \rangle , \langle M_2 \rangle ) \mid L(M_1) = L(M_2)\}$</p>

<p>$I= \{\langle M \rangle \mid \;\vert L(M) \vert = \infty \}$</p>

<p>I'm trying to Turing reduce $Q$ to $I$ ($Q \le_T I$), not the other way around as solved <a href="https://cs.sta... | complexity theory turing machines reductions | 1 | How to turing reduce equivalent languages $Q$ to infinite language $I$ -- (complexity theory turing machines reductions)
<p>Given two languages:</p>

<p>$Q= \{(\langle M_1 \rangle , \langle M_2 \rangle ) \mid L(M_1) = L(M_2)\}$</p>

<p>$I= \{\langle M \rangle \mid \;\vert L(M) \vert = \infty \}$</p>
... | habedi/stack-exchange-dataset |
45,111 | What is the name of the following algorithm? | <p>I am using the following algorithm to solve an optimization problem I have. I was wondering if there is a proper name for this algorithm in the literature. </p>

<p>Let $f(x)$ be my objective function.</p>

<p>I guess some $x_0$ and see have it performs.</p>

<p>Next, I <strong>randomly</str... | algorithms | 1 | What is the name of the following algorithm? -- (algorithms)
<p>I am using the following algorithm to solve an optimization problem I have. I was wondering if there is a proper name for this algorithm in the literature. </p>

<p>Let $f(x)$ be my objective function.</p>

<p>I guess some $x_0$ and see ha... | habedi/stack-exchange-dataset |
45,112 | Binary tree algorithm asymptotic analysis problem | <p>Assume we have a perfectly balanced Binary tree.
We have the following algorithm: <strong><em>For each passed node, traverse through all its ancestors and then do the same algorithm for the left and right child of the node.</em></strong></p>

<p>So, the way I try to find the Big-O complexity is this: The... | algorithms complexity theory asymptotics binary trees | 1 | Binary tree algorithm asymptotic analysis problem -- (algorithms complexity theory asymptotics binary trees)
<p>Assume we have a perfectly balanced Binary tree.
We have the following algorithm: <strong><em>For each passed node, traverse through all its ancestors and then do the same algorithm for the left and right... | habedi/stack-exchange-dataset |
45,121 | Is $H_0$ reducible to $\overline H_0$? | <p>Be $H_0$ the special halting problem with
$$H_0 = \lbrace \langle M \rangle \in \lbrace 0,1 \rbrace^* | \varepsilon \in L(M)\rbrace$$
and $\overline{H_0}$ being its complement.
Is $H_0$ reducible to $\overline{H_0}$? 
$$H_0 \leq \overline{H_0}$$
<br/>
I guess that this is not possible as $\ov... | computability turing machines reductions | 1 | Is $H_0$ reducible to $\overline H_0$? -- (computability turing machines reductions)
<p>Be $H_0$ the special halting problem with
$$H_0 = \lbrace \langle M \rangle \in \lbrace 0,1 \rbrace^* | \varepsilon \in L(M)\rbrace$$
and $\overline{H_0}$ being its complement.
Is $H_0$ reducible to $\overline{H_0}$? &#x... | habedi/stack-exchange-dataset |
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