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There are polynomial time algorithms to find maximum weighted matching in a general graph. Is there any algorithm that also handles negative weights in the general graph and find maximum weighted matching for that graph with negative weights ?
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|algorithms|graphs|matching| |
In context of data mining, what does it mean for an association rule measure to be maximal?
I cannot understand the term maximal in this context.
I know of maximal independent sets in algorithms but cannot make out this term. |
In context of data mining, what does it mean for an association rule measure to be maximal? |
|data-mining| |
{"Voters":[{"Id":867,"DisplayName":"AJed"}]} |
{"Voters":[{"Id":867,"DisplayName":"AJed"}]} |
I was reading about counting principle related to TOC. I understand that the set of TMs are countable infinity. I couldn't understand the significance of it. What is its not countable? |
If set of Tms is not countable? |
|computability|turing-machines|uncountability|church-turing-thesis| |
- Sequence - Order is important
- Set - Order is not important
Unlike set same element can appear multiple times in a sequence.
[Wikipedia article][1] gives more than enough information about this.
[1]: http://en.wikipedia.org/wiki/Sequence |
If set of TM's is not countable? |
The set of all languages is uncountable, hence there can't be a TM for every language, and there must be languages that aren't recursively enumerable. |
To expand a bit Luke's answer -
the main question is what problems (=languages) can be solved by a computer (=TM).
One might think that **any** problem can be solved by a computer. But this is not true. The reason is that there are such and such different Turing Machines, and **way more** different languages. Ther... |
Your question uses a number of words, such as "*logic*" that might require clarification. In order to answer I should start with some preliminary definitions.
Consider a universe of objects. The objects have different properties. We do not know yet if each object can be identified. We say that all objects that share... |
Your question uses a number of words, such as "*logic*" that might require clarification. In order to answer I should start with some preliminary definitions.
Consider a universe of objects. The objects have different properties. We do not know yet if each object can be identified. We say that all objects that share... |
Your question uses a number of words, such as "*logic*" that might require clarification. In order to answer I should start with some preliminary definitions.
Consider a universe of objects. The objects have different properties. We do not know yet if each object can be identified. We say that all objects that share... |
Say I have numbers with known factorizations $n = \prod \limits _i p_i ^{n_i}$ and $m = \prod \limits _i p_i ^{m_i}$ (where $p_i$ is the $i$th prime).
How hard is it to factorize $m+n$? Is there a more intelligent algorithm than if factorizations of $m$ and $n$ were not known? Assume $n$ and $m$ coprime as it is tr... |
How hard is it to factorize sum of two numbers |
|complexity-theory|factoring| |
I have a system in existence which works on parent-child model.
1. They share common attributes, as they belong to same class.
2. A parent can enforces certain data on any user selected attribute, and the data is required to be propagated down the hierarchy for the same attribute in all children and their children.... |
Optimizantion of Hierarchical Data Propagation |
|algorithms|databases|performance| |
I am new to discrete mathematics and the theory of computation I am trying to learn and understand the terminology.
I am having a difficult time understanding the difference between a set and a sequence. I understand that unlike a set, in a sequence order and repetition does matter and sequences contain objects rat... |
null |
An ambiguous Language is a formal language for which there exists a string that can have more than one meaning (several possible meanings or interpretations). Multiple synthesis structures for a string.
**[Question]**
Are Roman numbers an example of an ambiguous language?
Because there can be more then one... |
A function is $(\varepsilon, t)$-collision resistant if there is no boolean circuit (using "not", "and", "or") of size at most $t$ which outputs a collision with probability at least $\varepsilon$.
Let $h_0:\{0,1\}^{2m}\rightarrow\{0,1\}^m$ be a $(\varepsilon, t)$-collision resistant hash function and $i\in\mathbb{N... |
Collision resistant hash function |
|cryptography|hash| |
The birthday attack applies to any hash-function, regardless of its structure, and also to $h_i$.
For your first question, here is a possible hint. Note that
* if we can find a collision in $h_i$ then we can find a collision in $h_0$ (by considering the top-most $h_0$, for instance).
* if we can find a collisi... |
|graphs|bipartite-matching| |
|algorithms|graphs|approximation|matching| |
Consider we have a $k$D array $A$ filled with $0$ and $1$'s. $k$ is a constant. The dimension of the array is $d_1\times\ldots\times d_k$. Let $N = \prod_{i=1}^k d_i$. We want to create a data structure by preprocess $A$. The data structure allow one to query a $k$D box in $A$ and return
1. If there exist a $1$ in ... |
null |
In the case of Directed Hamiltonian Cycle, when you have a solution to the restricted case (the graph with arcs going both ways), the solution is a valid solution for the original problem. In the case of subset sum, a solution to the Real Subset Sum is not a solution for the Subset Sum.
In the first case, you are s... |
I was reading a few notes on Proof by Restriction and I am confused:
A Valid Proof by Restriction is the following:
Directed Hamiltonian Cycle Problem is NP Complete because if we look only at _instances_ of DHC where For $G=(V,E)\quad (u,v)\in E \leftrightarrow (v,u) \in E$ then it reduces to Hamiltonian Cycle w... |
Simple NP Complete Question [Proof By Restriction] |
|untagged| |
Think about the set of all possible instances of DHC. A subset of these instances are those where, for every directed edge $(u, v)$, there is always a matching directed edge $(v, u)$. (In general, this doesn't have to be the case, but it CAN be the case, which is why this is a valid restriction.)
Now think about the... |
null |
A proof that P = NP might get accepted by a mathematical journal, but it will never be accepted by the elite professionals. The reasons is that they know that P != NP (at least for all practical purposes). They also know that it is unbelievable difficult to prove this, so even a proof that P != NP will be received with... |
|complexity-theory|np-complete| |
|complexity-theory|np-complete|proof-techniques| |
What you have in the case of DHC is really just a reduction: assuming you could solve DHC in polynomial time, you can solve HC in polynomial time, too, because it is a special case (use the same algorithm!). Therefore, HC $\in$ NPC implies DHC $\in$ NPC.
If you think of it in terms of the usual reduction HC $\leq_p$... |
|complexity-theory|p-vs-np| |
With the advent of [BWAPI][1], many AI enthusiasts have been making amazing AIs that can compete against top players in Starcraft. This led me to wonder if RTS (Real-Time Strategy) games can ever be solved theoretically.
One of my colleague argues no, because RTS games are non-deterministic and stochastic. What doe... |
Can Real-Time Strategy games be ever solved? |
|artificial-intelligence| |
I was reading a few notes on Proof by Restriction and I am confused:
A Valid Proof by Restriction is the following:
Directed Hamiltonian Cycle Problem is NP Complete because if we look only at _instances_ of DHC where For $G=(V,E)\quad (u,v)\in E \leftrightarrow (v,u) \in E$ then it reduces to Hamiltonian Cycle w... |
|artificial-intelligence|computer-games| |
Proof by restriction: when is it valid to restrict to a special case? |
null |
The best example I have is the poor user who had a file named `.. -r` and typed in `rm *`.
Whether this story is true or not, it's become a Unix hater's classic.
See http://en.wikipedia.org/wiki/The_Unix-Haters_Handbook , which has an introduction by Dennis Ritchie himself, for lots of these examples.
I'll add... |
**Claim:** Yes, that statement is true.
**Proof Sketch:** Let $T_1,T_2$ be two minimal spanning trees with edge-weight multisets $W_1,W_2$. Assume $W_1 \neq W_2$ and denote their [symmetric difference](https://en.wikipedia.org/wiki/Symmetric_difference) with $W = W_1 \mathop{\Delta} W_2$.
Choose edge $e \in T_1 ... |
|algorithms|reference-request|education|bioinformatics| |
null |
|data-structures|runtime-analysis|heaps|amortized-analysis| |
|algorithms|optimization|dynamic-programming|linear-programming| |
|algorithms|graphs|runtime-analysis|spanning-trees| |
|logic|linear-temporal-logic| |
I believe that in the context of [that paper (PS)][1], you can read "maximal" as "maximized". That is to say, the conviction function $P(A)P(\neg B)/P(A, \neg B)$ attains its greatest value when $A \implies B$.
[1]: http://infolab.stanford.edu/~sergey/dic.ps |
The best example I have is the poor user who had a file named `.. -r` and typed in `rm *`.
Whether this story is true or not, it's become a Unix hater's classic.
See [The Unix-Haters Handbook](http://en.wikipedia.org/wiki/The_Unix-Haters_Handbook), which has an introduction by Dennis Ritchie himself, for lots of ... |
As others told you: it depends a little on the book that you will be using, as well as on the topics taught. Sometimes it will be rather self explanatory. However in order to be better prepared (and get used to the terminology) look at some primers on the web, like [Preparata: A Biology Primer for Computer Scientists][... |
if a node terminates the algorithm after an iteration with probability $1/c$, then after $k$ iterations this probability is $c^{-k}$. and the number of iterations required is $\ln _c n$. This is done by arguing that the expected number of nodes after $k$ iterations is $n c ^{-k}$, and we want to make this value less or... |
I took a course on compilers in my undergraduate studies in which we wrote a compiler that compiles source programs in a toy Java-like language to a toy assembly language (for which we had an interpreter). In the project we made some assumptions about the target machine closely related to "real" native executables, inc... |
Theoretical minimum number of registers for a modern computer? |
|compilers|computer-architecture| |
If you allow direct memory access by memory address, then you do not need any "registers" because you can use memory locations instead. For example, memory at location 0 can be the program counter, at location 1 we have the stack pointer, etc. But that is cheating.
So to prevent ourselves from cheating, let us assum... |
Hope the question is right at CS. [Wikipedia][1] explains CSMA/CD. A collision seems to cause the wave of the outgoing signal and the wave of the incoming signal to overlap. Thus, the signal has values with more amplitude than allowed for a "1-bit". This could be used as a working collision detection algorithm.
Howe... |
Jamming signal useless in CSMA / CD? |
|algorithms|computer-networks| |
I already understood how the well-known algorithms like Graham, Quickhull etc. work, but i have difficulties in understanding 2 naive versions of convex hull algorithms:
Let S={p1, ..., pn} a set of points and CH(S) the convex hull of S.
("any_sentence" is a quote from different course books.)
<hr/>
**A1)... |
naive convex hull algorithms |
|computational-geometry| |
**A1)** You're right, the algorithm description sounds kind of weird. A naive algorithm that takes exponential time would rather be something like
foreach (R in S.subsets)
if (R.isConvexHull(S))
return R
However, the method for checking whether R is a convex hull needs $n$ time, so we obtain a r... |
null |
I am researching collaborative editing systems for some work, but so far my search is turning up blank.
Collaborative real-time editing systems almost all have features like:
* Many users can edit the document at the same time
* All changes are dated and saved in a linear revision history
* Edits are visible in... |
What sort of algorithm/communication model/data structure do collaborative real time editors use? |
|data-structures| |
|data-structures|efficiency| |
|computer-networks|encoding-scheme| |
The interesting question is: what is the alternative? The only other method I know is testing/benchmarking. We program the algorithms, let them run on (a representative sample of) the finite input set and compare the results. There are a couple of problems with that.
* The results are not general in terms of machin... |
I would like to know in which classification is the R programming language. It has elements of the imperative paradigm and object oriented paradigm (some things like that even a number is an object and they can be freely mixed). I am not quite sure if it has functional programming characteristics. So it can be consider... |
which would be the classification of R language according to paradigms? |
|programming-languages| |
null |
Consider we have a $k$D array $A$ filled with $0$ and $1$'s. $k$ is a constant. The dimension of the array is $d_1\times\ldots\times d_k$. Let $N = \prod_{i=1}^k d_i$. We want to create a data structure by preprocess $A$. The data structure allow one to query a $k$D box in $A$ and return
1. If there exist a $1$ in ... |
Consider we have a $k$D array $A$ filled with $0$ and $1$'s. $k$ is a constant. The dimension of the array is $d_1\times\ldots\times d_k$. Let $N = \prod_{i=1}^k d_i$. We want to create a data structure by preprocess $A$. The data structure allow one to query a $k$D box in $A$ and return
1. If there exist a $1$ in ... |
Wave overlaps need not cause just 1-bits with a too high amplitude. They could also flip bits around, or nullify each other. Thus error correction is not as easy as you describe and one actually has to use some kind of checksumming like CRC to detect errors reliably. |
I Hope that this question is right at CS. [Wikipedia][1] explains CSMA/CD. A collision seems to cause the wave of the outgoing signal and the wave of the incoming signal to overlap. Thus, the signal has values with more amplitude than allowed for a "1-bit". This could be used as a working collision detection algorithm.... |
null |
I'm looking at collision detection in communication protocols, in particular [Carrier sense multiple access with collision detection (CSMA/CD)][1]. According to what I've read on Wikipedia, a collision seems to cause the wave of the outgoing signal and the wave of the incoming signal to overlap. Thus, the signal has va... |
|computer-networks|communication-protocols|encoding-scheme| |
MST is actually a tree, not a path (generally). Therefore, it is not a solution to TSP. (Although, MST can help you to find a solution that is not more than twice as long as the optimal solution, if you solve this in a metric space on a complete graph. That's unrelated story.)
Now, I must admit that I do not see a w... |
[It looks like](http://code.google.com/p/bwapi/issues/detail?id=423) there are elements of (pseudo)randomness in the game.
Of course, this does not seem like a major property and you can ask for solving the game without this feature. Then you end up with a very deep game tree that probably does not have any nice mat... |
[It looks like](http://code.google.com/p/bwapi/issues/detail?id=423) there are elements of (pseudo)randomness in StarCraft.
Of course, this does not seem like a major property and you can ask for solving the game without this feature. Then you end up with a very deep game tree that probably does not have any nice ma... |
Let $B$ be a boolean formula consisting of the usual AND, OR, and NOT operators and some atoms. I would like to count the number of satisfying assignments for $B$. That is, I want to find the number of different assignments of truth values to the atoms of $B$ for which $B$ assumes a true value. For example, the formul... |
Is there a sometimes-efficient algorithm to compute the number of satisfying assignments to a boolean formula? |
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