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In this paper, we develop new tools and connections for exponential time approximation. In this setting, we are given a problem instance and a parameter $\alpha>1$, and the goal is to design an $\alpha$-approximation algorithm with the fastest possible running time. |
We consider the online $k$-taxi problem, a generalization of the $k$-server problem, in which $k$ taxis serve a sequence of requests in a metric space. A request consists of two points $s$ and $t$, representing a passenger that wants to be carried by a taxi from $s$ to $t$. |
It is shown that a context-free grammar of size $m$ that produces a single string $w$ (such a grammar is also called a string straight-line program) can be transformed in linear time into a context-free grammar for $w$ of size $\mathcal{O} (m)$, whose unique derivation tree has depth $\mathcal{O}(\log |w|)$. |
We study algorithms for the Submodular Multiway Partition problem (SubMP). An instance of SubMP consists of a finite ground set $V$, a subset of $k$ elements $S = \{s_1,s_2,...,s_k\}$ called terminals, and a non-negative submodular set function $f:2^V\rightarrow \mathbb{R}_+$ on $V$ provided as a value oracle. |
We show optimal lower bounds for spanning forest computation in two different models: <br>* One wants a data structure for fully dynamic spanning forest in which updates can insert or delete edges amongst a base set of $n$ vertices. The sole allowed query asks for a spanning forest, which the data structure should suc... |
Markov decision processes (MDP) are useful to model concurrent process optimisation problems, but verifying them with numerical methods is often intractable. Existing approximative approaches do not scale well and are limited to memoryless schedulers. |
We present a framework for deterministically rounding a dynamic fractional matching. Applying our framework in a black-box manner on top of existing fractional matching algorithms, we derive the following new results: (1) The first deterministic algorithm for maintaining a $(2-\delta)$-approximate maximum matching in ... |
Stabbing queries in sets of intervals are usually answered using segment trees. A dynamic variant of segment trees has been presented by van Kreveld and Overmars, which uses red-black trees to do rebalancing operations. |
The first worst-case linear-time algorithm for selection was discovered in 1973; however, linear-time binary heap construction was first published in 1964. Here we describe another worst-case linear selection algorithm,which is simply implemented and uses binary heap construction as its principal engine. |
I give an introduction to algorithmic uses of the principle of inclusion-exclusion. The presentation is intended to be be concrete and accessible, at the expense of generality and comprehensiveness. |
In phylogenetics, a central problem is to infer the evolutionary relationships between a set of species $X$; these relationships are often depicted via a phylogenetic tree -- a tree having its leaves univocally labeled by elements of $X$ and without degree-2 nodes -- called the "species tree". One common appro... |
Counting perfect matchings has played a central role in the theory of counting problems. The permanent, corresponding to bipartite graphs, was shown to be #P-complete to compute exactly by Valiant (1979), and a fully polynomial randomized approximation scheme (FPRAS) was presented by Jerrum, Sinclair, and Vigoda (2004... |
We show that every $H$-minor-free graph has a light $(1+\epsilon)$-spanner, resolving an open problem of Grigni and Sissokho and proving a conjecture of Grigni and Hung. Our lightness bound is \[O\left(\frac{\sigma_H}{\epsilon^3}\log \frac{1}{\epsilon}\right)\] where $\sigma_H = |V(H)|\sqrt{\log |V(H)|}$ is the sparsi... |
In the framework of graph property testing, we study the problem of determining if a graph admits a cluster structure. We say that a graph is $(k, \phi)$-clusterable if it can be partitioned into at most $k$ parts such that each part has conductance at least $\phi$. |
The suffix array is a data structure that finds numerous applications in string processing problems for both linguistic texts and biological data. It has been introduced as a memory efficient alternative for suffix trees. |
In theoretical computer science, it is a common practice to show existential lower bounds for problems, meaning there is a family of pathological inputs on which no algorithm can do better. However, most inputs of interest can be solved much more efficiently, giving rise to the notion of universally optimal algorithms... |
This paper deals with the problem of finding a collection of vertex-disjoint paths in a given graph G=(V,E) such that each path has at least four vertices and the total number of vertices in these paths is maximized. The problem is NP-hard and admits an approximation algorithm which achieves a ratio of 2 and runs in O... |
The parameterized complexity of problems is often studied with respect to the size of their optimal solutions. However, for a maximization problem, the size of the optimal solution can be very large, rendering algorithms parameterized by it inefficient. |
We study the store-and-forward packet routing problem for simultaneous multicasts, in which multiple packets have to be forwarded along given trees as fast as possible. <br>This is a natural generalization of the seminal work of Leighton, Maggs and Rao, which solved this problem for unicasts, i.e. the case where all t... |
We give a polynomial-time approximation scheme for the generalization of Huffman Coding in which codeword letters have non-uniform costs (as in Morse code, where the dash is twice as long as the dot). The algorithm computes a (1+epsilon)-approximate solution in time O(n + f(epsilon) log^3 n), where n is the input size... |
We study quantum algorithms for several fundamental string problems, including Longest Common Substring, Lexicographically Minimal String Rotation, and Longest Square Substring. These problems have been widely studied in the stringology literature since the 1970s, and are known to be solvable by near-linear time class... |
We study the density estimation problem defined as follows: given $k$ distributions $p_1, \ldots, p_k$ over a discrete domain $[n]$, as well as a collection of samples chosen from a ``query'' distribution $q$ over $[n]$, output $p_i$ that is ``close'' to $q$. Recently~\cite{aamand2023data} gave the fir... |
The classical analysis of online algorithms, due to its worst-case nature, can be quite pessimistic when the input instance at hand is far from worst-case. Often this is not an issue with machine learning approaches, which shine in exploiting patterns in past inputs in order to predict the future. |
This paper discusses the fixed-hub single allocation problem (FHSAP). In this problem, a network consists of hub nodes and terminal nodes. |
Given an array A containing arbitrary (positive and negative) numbers, we consider the problem of supporting range maximum-sum segment queries on A: i.e., given an arbitrary range [i,j], return the subrange [i' ,j' ] \subseteq [i,j] such that the sum of the numbers in A[i'..j'] is maximized. Chen and C... |
We give a polynomial time algorithm for the lossy population recovery problem. In this problem, the goal is to approximately learn an unknown distribution on binary strings of length $n$ from lossy samples: for some parameter $\mu$ each coordinate of the sample is preserved with probability $\mu$ and otherwise is repl... |
In the field of parameterized complexity theory, the study of graph width measures has been intimately connected with the development of width-based model checking algorithms for combinatorial properties on graphs. In this work, we introduce a general framework to convert a large class of width-based model-checking al... |
The aim of this note is to provide a reduction of the Exact Matching problem to the Top-$k$ Perfect Matching Problem. Together with earlier work by El Maalouly, this shows that the two problems are polynomial-time equivalent. |
We study an algorithm for approximating the multivariate independence polynomial $Z(\mathbf{z})$, with negative and complex arguments, an object that has strong connections to combinatorics and to statistical physics. In particular, the independence polynomial with negative arguments, $Z(-\mathbf{p})$, determines the ... |
Bin packing is an algorithmic problem that arises in diverse applications such as remnant inventory systems, shipping logistics, and appointment scheduling. In its simplest variant, a sequence of $T$ items (e.g., orders for raw material, packages for delivery) is revealed one at a time, and each item must be packed on... |
We consider the bit-probe complexity of the set membership problem, where a set S of size at most n from a universe of size m is to be represented as a short bit vector in order to answer membership queries of the form "Is x in S? " by adaptively probing the bit vector at t places. |
There are many indexes (measures or metrics) in Social Network Analysis (SNA), like density, cohesion, etc. In this paper, we define a new SNA index called "comfortability". |
We consider the Work Function Algorithm for the k-server problem. We show that if the Work Function Algorithm is c-competitive, then it is also strictly (2c)-competitive. |
We study the complexity of graph modification problems with respect to homomorphism-based colouring properties of edge-coloured graphs. A homomorphism from edge-coloured graph $G$ to edge-coloured graph $H$ is a vertex-mapping from $G$ to $H$ that preserves adjacencies and edge-colours. |
The Massive Parallel Computation (MPC) model is a theoretical framework for popular parallel and distributed platforms such as MapReduce, Hadoop, or Spark. We consider the task of computing a large matching or small vertex cover in this model when the space per machine is $n^\delta$ for $\delta \in (0,1)$, where $n$ i... |
Online load balancing for heterogeneous machines aims to minimize the makespan (maximum machine workload) by scheduling arriving jobs with varying sizes on different machines. In the adversarial setting, where an adversary chooses not only the collection of job sizes but also their arrival order, the problem is well-u... |
Parameter inference is a fundamental problem in data-driven modeling. Given observed data that is believed to be a realization of some parameterized model, the aim is to find parameter values that are able to explain the observed data. |
An ancestry labeling scheme assigns labels (bit strings) to the nodes of rooted trees such that ancestry queries between any two nodes in a tree can be answered merely by looking at their corresponding labels. The quality of an ancestry labeling scheme is measured by its label size, that is the maximal number of bits ... |
Two-stage bipartite matching is a fundamental problem of optimization under uncertainty introduced by Feng, Niazadeh, and Saberi (2021), who study it under the stochastic and adversarial paradigms of uncertainty. We propose a method to interpolate between these paradigms, using the Algorithms with Predictions (ALPS) f... |
We consider the problem of finding a basis of a matroid with weight exactly equal to a given target. Here weights can be discrete values from $\{-\Delta,\ldots,\Delta\}$ or more generally $m$-dimensional vectors of such discrete values. |
There are several known data structures that answer distance queries between two arbitrary vertices in a planar graph. The tradeoff is among preprocessing time, storage space and query time. |
We give a polynomial-time algorithm for the problem of robustly estimating a mixture of $k$ arbitrary Gaussians in $\mathbb{R}^d$, for any fixed $k$, in the presence of a constant fraction of arbitrary corruptions. This resolves the main open problem in several previous works on algorithmic robust statistics, which ad... |
Real-world graphs often manifest as a massive temporal stream of edges. The need for real-time analysis of such large graph streams has led to progress on low memory, one-pass streaming graph algorithms. |
We introduce the problem of $k$-chasing of convex functions, a simultaneous generalization of both the famous k-server problem in $R^d$, and of the problem of chasing convex bodies and functions. Aside from fundamental interest in this general form, it has natural applications to online $k$-clustering problems with ob... |
In this paper, we consider classic randomized low diameter decomposition procedures for planar graphs that obtain connected clusters which are cohesive in that close-by pairs of nodes are assigned to the same cluster with high probability. We require the additional aspect of individual fairness - pairs of nodes at com... |
We provide the first nearly-linear time algorithm for approximating $\ell_{q \rightarrow p}$-norms of non-negative matrices, for $q \geq p \geq 1$. Our algorithm returns a $(1-\varepsilon)$-approximation to the matrix norm in time $\widetilde{O}\left(\frac{1}{q \varepsilon} \cdot \text{nnz}(\boldsymbol{\mathit{A}})\ri... |
We study the communication complexity and streaming complexity of approximating unweighted semi-matchings. A semi-matching in a bipartite graph G = (A, B, E), with n = |A|, is a subset of edges S that matches all A vertices to B vertices with the goal usually being to do this as fairly as possible. |
An algorithm is given for determining an optimal $b$-step approximation of weighted data, where the error is measured with respect to the $L_\infty$ norm. For data presorted by the independent variable the algorithm takes $\Theta(n + \log n \cdot b(1+\log n/b))$ time and $\Theta(n)$ space. |
Graph clustering is a fundamental problem in unsupervised learning, with numerous applications in computer science and in analysing real-world data. In many real-world applications, we find that the clusters have a significant high-level structure. |
We study a graph partition problem where we are given a directed acyclic graph (DAG) whose vertices and arcs can be respectively regarded as tasks and dependencies among tasks. The objective of the problem is to minimize the total energy consumed for completing these tasks by assigning the tasks to k heterogeneous mac... |
Given n jobs with release dates, deadlines and processing times we consider the problem of scheduling them on m parallel machines so as to minimize the total energy consumed. Machines can enter a sleep state and they consume no energy in this state. |
In this paper, we apply a Threshold-Decreasing Algorithm to maximize $k$-submodular functions under a matroid constraint, which reduces the query complexity of the algorithm compared to the greedy algorithm with little loss in approximation ratio. We give a $(\frac{1}{2} - \epsilon)$-approximation algorithm for monoto... |
The \emph{Product Structure Theorem} for planar graphs (Dujmović et al. \ \emph{JACM}, \textbf{67}(4):22) states that any planar graph is contained in the strong product of a planar $3$-tree, a path, and a $3$-cycle. |
We show that the dominating set problem admits a constant factor approximation in a constant number of rounds in the LOCAL model of distributed computing on graph classes with bounded expansion. This generalizes a result of Czygrinow et al. for graphs with excluded topological minors. |
The weighted ancestor problem is a well-known generalization of the predecessor problem to trees. It is known to require $\Omega(\log\log n)$ time for queries provided $O(n\mathop{\mathrm{polylog}} n)$ space is available and weights are from $[0..n]$, where $n$ is the number of tree nodes. |
We study the Directed Feedback Vertex Set problem parameterized by the treewidth of the input graph. We prove that unless the Exponential Time Hypothesis fails, the problem cannot be solved in time $2^{o(t\log t)}\cdot n^{\mathcal{O}(1)}$ on general directed graphs, where $t$ is the treewidth of the underlying undirec... |
In the field of interactive coding, two or more parties wish to carry out a distributed computation over a communication network that may be noisy. The ultimate goal is to develop efficient coding schemes that can tolerate a high level of noise while increasing the communication by only a constant factor (i.e., consta... |
Planar Embedding is a drawing of a graph on the plane such that the edges do not intersect each other except at the vertices. We know that testing the planarity of a graph and computing its embedding (if it exists), can efficiently be computed, both sequentially [HT] and in parallel [RR94], when the entire graph is pr... |
We consider a maximum entropy edge weight model for shortest path networks that allows for negative weights. Given a graph $G$ and possible weights $\mathcal{W}$ typically consisting of positive and negative values, the model selects edge weights $w \in \mathcal{W}^m$ uniformly at random from all weights that do not i... |
We introduce the first grammar-compressed representation of a sequence that supports searches in time that depends only logarithmically on the size of the grammar. Given a text $T[1..u]$ that is represented by a (context-free) grammar of $n$ (terminal and nonterminal) symbols and size $N$ (measured as the sum of the l... |
The problem of finding maximum (or minimum) witnesses of the Boolean product of two Boolean matrices (MW for short) has a number of important applications, in particular the all-pairs lowest common ancestor (LCA) problem in directed acyclic graphs (dags). The best known upper time-bound on the MW problem for n\times n... |
In this paper we consider the problem of efficiently computing $\epsilon$-sketches for the Laplacian and its pseudoinverse. Given a Laplacian and an error tolerance $\epsilon$, we seek to construct a function $f$ such that for any vector $x$ (chosen obliviously from $f$), with high probability $(1-\epsilon) x^\top A x... |
We study the problem of finding a spanning forest in an undirected, $n$-vertex multi-graph under two basic query models. One is the Linear query model which are linear measurements on the incidence vector induced by the edges; the other is the weaker OR query model which only reveals whether a given subset of plausibl... |
A skeleton Huffman tree is a Huffman tree in which all disjoint maximal perfect subtrees are shrunk into leaves. Skeleton Huffman trees, besides saving storage space, are also used for faster decoding and for speeding up Huffman-shaped wavelet trees. |
We prove two dichotomy results for detecting long paths as patterns in a given graph. The NP-hard problem Longest Induced Path is to determine the longest induced path in a graph. |
In this note, we revisit the recursive random contraction algorithm of Karger and Stein for finding a minimum cut in a graph. Our revisit is occasioned by a paper of Fox, Panigrahi, and Zhang which gives an extension of the Karger-Stein algorithm to minimum cuts and minimum $k$-cuts in hypergraphs. |
To provide quick responses to users, Internet companies rely on online data systems able to answer queries in milliseconds. These systems employ complementary overload management techniques to ensure they provide a continued, acceptable service through-out traffic surges, where 'acceptable' partly means that s... |
As advances in technology allow for the collection, storage, and analysis of vast amounts of data, the task of screening and assessing the significance of discovered patterns is becoming a major challenge in data mining applications. In this work, we address significance in the context of frequent itemset mining. |
Instance-optimized components have made their way into production systems. To some extent, this adoption is due to the characteristics of customer workloads, which can be individually leveraged during the model training phase. |
Knowledge can be represented compactly in a multitude ways, from a set of propositional formulas, to a Kripke model, to a database. In this paper we study the aggregation of information coming from multiple sources, each source submitting a database modelled as a first-order relational structure. |
Differentially-private (DP) databases allow for privacy-preserving analytics over sensitive datasets or data streams. In these systems, user privacy is a limited resource that must be conserved with each query. |
To retrieve the best results in a database we use Top-K queries and Skyline queries but some problems arise. The formers rely too much on user preferences, which are difficult to quantify and may skew the fetching of the data, while the latters tend to output too much data. |
With the advance of Web Services technologies and the emergence of Web Services into the information space, tremendous opportunities for empowering users and organizations appear in various application domains including electronic commerce, travel, intelligence information gathering and analysis, health care, digital g... |
This paper introduces RG (Relational Genetic) model, a revised relational model to represent graph-structured data in RDBMS while preserving its topology, for efficiently and effectively extracting data in different formats from disparate sources. Along with: |
While deep neural networks (DNNs) are an increasingly popular way to query large corpora of data, their significant runtime remains an active area of research. As a result, researchers have proposed systems and optimizations to reduce these costs by allowing users to trade off accuracy and speed. |
Ongoing time point now is used to state that a tuple is valid from the start point onward. For database systems ongoing time points have far-reaching implications since they change continuously as time passes by. |
Cloud-based data analysis is nowadays common practice because of the lower system management overhead as well as the pay-as-you-go pricing model. The pricing model, however, is not always suitable for query processing as heavy use results in high costs. |
The past two decades have witnessed significant success in applying columnar storage to data warehousing and analytics. However, the rapid growth of machine learning poses new challenges. |
Configuration knobs of database systems are essential to achieve high throughput and low latency. Recently, automatic tuning systems using machine learning methods (ML) have shown to find better configurations compared to experienced database administrators (DBAs). |
Discriminative pattern mining is a data mining task in which we find patterns that distinguish transactions in the class of interest from those in other classes, and is also called emerging pattern mining or subgroup discovery. One practical problem in discriminative pattern mining is how to handle numeric values in t... |
Schema matching constitutes a pivotal phase in the data ingestion process for contemporary database systems. Its objective is to discern pairwise similarities between two sets of attributes, each associated with a distinct data table. |
Modern in-memory databases are typically used for high-performance workloads, therefore they have to be optimized for small memory footprint and high query speed at the same time. Data compression has the potential to reduce memory requirements but often reduces query speed too. |
This paper investigates user preferences for Linear Top-k Queries and Directional Top-k Queries, two methods for ranking results in multidimensional datasets. While Linear Queries prioritize weighted sums of attributes, Directional Queries aim to deliver more balanced results by incorporating the spatial relationship ... |
Relational Database Management Systems designed for Online Analytical Processing (RDBMS-OLAP) have been foundational to democratizing data and enabling analytical use cases such as business intelligence and reporting for many years. However, RDBMS-OLAP systems present some well-known challenges. |
We study three different kinds of embeddings of tree patterns: weakly-injective, ancestor-preserving, and lca-preserving. While each of them is often referred to as injective embedding, they form a proper hierarchy and their computational properties vary (from P to NP-complete). |
Database management has become an enormous tool for on-demand content distribution services, proffering required information and providing custom services to the user. Also plays a major role for the platforms to manage their data in such a way that data redundancy is minimized. |
We present a formal semantics and proof of soundness for shapes schemas, an expressive schema language for RDF graphs that is the foundation of Shape Expressions Language 2.0. It can be used to describe the vocabulary and the structure of an RDF graph, and to constrain the admissible properties and values for nodes in... |
Complex logical query answering (CLQA) is a recently emerged task of graph machine learning that goes beyond simple one-hop link prediction and solves a far more complex task of multi-hop logical reasoning over massive, potentially incomplete graphs in a latent space. The task received a significant traction in the co... |
Many modern navigation systems and map-based services do not only provide the fastest route from a source location s to a target location t but also provide a few alternative routes to the users as more options to choose from. Consequently, computing alternative paths has received significant research attention. |
For light curve generation, a pre-planned photometry survey is needed nowadays, where all of the exposure coordinates have to be given and don't change during the survey. This thesis shows it is not required and we can data-mine these light curves from astronomical data that was never meant for this purpose. |
Query optimizers are a performance-critical component in every database system. Due to their complexity, optimizers take experts months to write and years to refine. |
Transactional isolation guarantees are crucial for database correctness. However, recent studies have uncovered numerous isolation bugs in production databases. |
Current and future astronomical surveys are producing catalogs with millions and billions of objects. On-line access to such big datasets for data mining and cross-correlation is usually as highly desired as unfeasible. |
As random walk is a powerful tool in many graph processing, mining and learning applications, this paper proposes an efficient in-memory random walk engine named ThunderRW. Compared with existing parallel systems on improving the performance of a single graph operation, ThunderRW supports massive parallel random walks... |
We present WiscSort, a new approach to high-performance concurrent sorting for existing and future byte-addressable storage (BAS) devices. WiscSort carefully reduces writes, exploits random reads by splitting keys and values during sorting, and performs interference-aware scheduling with thread pool sizing to avoid I/... |
In this paper, we investigate the problem of computing a multiway join in one round of MapReduce when the data may be skewed. We optimize on communication cost, i.e., the amount of data that is transferred from the mappers to the reducers. |
Safety and mission performance validation of autonomous vehicles (AVs) is a major challenge. In this paper we describe a methodology for constructing and applying assertion checks to validate the behaviour of an AV operating either in simulation or in the real world. |
In the era of information explosion, facing complex information, it is difficult for users to choose the information of interest, and businesses also need detailed information on ways to let the ad stand out. By this time, it is recommended that a good way. |
Semantic Web technology has successfully facilitated many RDF models with rich data representation methods. It also has the potential ability to represent and store multimodal knowledge bases such as multimodal scene graphs. |
Change point detection has recently gained popularity as a method of detecting performance changes in software due to its ability to cope with noisy data. In this paper we present Hunter, an open source tool that automatically detects performance regressions and improvements in time-series data. |
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