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Vertex FaultTolerant Emulators arXiv.cs.DS Pub Date : 20210916
Greg Bodwin, Michael Dinitz, Yasamin NazariA $k$spanner of a graph $G$ is a sparse subgraph that preserves its shortest path distances up to a multiplicative stretch factor of $k$, and a $k$emulator is similar but not required to be a subgraph of $G$. A classic theorem by Thorup and Zwick [JACM '05] shows that, despite the extra flexibility available to emulators, the size/stretch tradeoffs for spanners and emulators are equivalent. Our main

A Quadratic Time Locally Optimal Algorithm for NPhard Equal Cardinality Partition Optimization arXiv.cs.DS Pub Date : 20210916
Kaan Gokcesu, Hakan GokcesuWe study the optimization version of the equal cardinality set partition problem (where the absolute difference between the equal sized partitions' sums are minimized). While this problem is NPhard and requires exponential complexity to solve in general, we have formulated a weaker version of this NPhard problem, where the goal is to find a locally optimal solution. The local optimality considered

Sublinear Time Eigenvalue Approximation via Random Sampling arXiv.cs.DS Pub Date : 20210916
Rajarshi Bhattacharjee, Cameron Musco, Archan RayWe study the problem of approximating the eigenspectrum of a symmetric matrix $A \in \mathbb{R}^{n \times n}$ with bounded entries (i.e., $\A\_{\infty} \leq 1$). We present a simple sublinear time algorithm that approximates all eigenvalues of $A$ up to additive error $\pm \epsilon n$ using those of a randomly sampled $\tilde{O}(\frac{1}{\epsilon^4}) \times \tilde O(\frac{1}{\epsilon^4})$ principal

Exact and Approximation Algorithms for ManyToMany Point Matching in the Plane arXiv.cs.DS Pub Date : 20210915
Sayan Bandyapadhyay, Anil Maheshwari, Michiel SmidGiven two sets $S$ and $T$ of points in the plane, of total size $n$, a {manytomany} matching between $S$ and $T$ is a set of pairs $(p,q)$ such that $p\in S$, $q\in T$ and for each $r\in S\cup T$, $r$ appears in at least one such pair. The {cost of a pair} $(p,q)$ is the (Euclidean) distance between $p$ and $q$. In the {minimumcost manytomany matching} problem, the goal is to compute a manytomany

A Characterization of IndividualizationRefinement Trees arXiv.cs.DS Pub Date : 20210915
Markus Anders, Jendrik Brachter, Pascal SchweitzerIndividualizationRefinement (IR) algorithms form the standard method and currently the only practical method for symmetry computations of graphs and combinatorial objects in general. Through backtracking, on each graph an IRalgorithm implicitly creates an IRtree whose order is the determining factor of the running time of the algorithm. We give a precise and constructive characterization which trees

Probabilistic Analysis of Euclidean Capacitated Vehicle Routing arXiv.cs.DS Pub Date : 20210914
Claire Mathieu, Hang ZhouWe give a probabilistic analysis of the unitdemand Euclidean capacitated vehicle routing problem in the random setting, where the input distribution consists of $n$ unitdemand customers modeled as independent, identically distributed uniform random points in the twodimensional plane. The objective is to visit every customer using a set of routes of minimum total length, such that each route visits

Minimum Path Star Topology Algorithms for Weighted Regions and Obstacles arXiv.cs.DS Pub Date : 20210914
Tyler King, Michael SoltysShortest path algorithms have played a key role in the past century, paving the way for modern day GPS systems to find optimal routes along static systems in fractions of a second. One application of these algorithms includes optimizing the total distance of power lines (specifically in star topological configurations). Due to the relevancy of discovering wellconnected electrical systems in certain

αIndirect Control in Onionlike Networks arXiv.cs.DS Pub Date : 20210915
Kirill Polovnikov, Nikita Pospelov, Dmitriy SkougarevskiyTens of thousands of parent companies control millions of subsidiaries through long chains ofintermediary entities in global corporate networks. Conversely, tens of millions of entities aredirectly held by sole owners. We propose an algorithm for identification of ultimate controllingentities in such networks that unifies direct and indirect control and allows for continuousinterpolation between the

Convergence of a HumanintheLoop PolicyGradient Algorithm With Eligibility Trace Under Reward, Policy, and Advantage Feedback arXiv.cs.DS Pub Date : 20210915
Ishaan Shah, David Halpern, Kavosh Asadi, Michael L. LittmanFluid humanagent communication is essential for the future of humanintheloop reinforcement learning. An agent must respond appropriately to feedback from its human trainer even before they have significant experience working together. Therefore, it is important that learning agents respond well to various feedback schemes human trainers are likely to provide. This work analyzes the COnvergent ActorCritic

Online kWay Matching with Delays and the HMetric arXiv.cs.DS Pub Date : 20210914
Darya Melnyk, Yuyi Wang, Roger WattenhoferIn this paper, we study $k$Way Mincost Perfect Matching with Delays  the $k$MPMD problem. This problem considers a metric space with $n$ nodes. Requests arrive at these nodes in an online fashion. The task is to match these requests into sets of exactly $k$, such that the space and time cost of all matched requests are minimized. The notion of the space cost requires a definition of an underlying

Optimizing the ecological connectivity of landscapes with generalized flow models and preprocessing arXiv.cs.DS Pub Date : 20210914
François Hamonic, Cécile Albert, Basile Couëtoux, Yann VaxèsIn this paper we consider the problem of optimizing the ecological connectivity of a landscape under a budget constraint by improving habitat areas and ecological corridors between them. We consider a formulation of this problem in terms of graphs in which vertices represent the habitat areas and arcs represent a probability of connection between two areas that depend on the quality of the respective

Distributed Vertex Cover Reconfiguration arXiv.cs.DS Pub Date : 20210914
Keren CensorHillel, Yannic Maus, Shahar RomemPeled, Tigran TonoyanReconfiguration schedules, i.e., sequences that gradually transform one solution of a problem to another while always maintaining feasibility, have been extensively studied. Most research has dealt with the decision problem of whether a reconfiguration schedule exists, and the complexity of finding one. A prime example is the reconfiguration of vertex covers. We initiate the study of batched vertex

Online Algorithms with Lookaround arXiv.cs.DS Pub Date : 20210914
Amirreza Akbari, Henrik Lievonen, Darya Melnyk, Joona Sarkijarvi, Jukka SuomelaWe introduce a new model of computation: the online LOCAL model (OLOCAL). In this model, the adversary reveals the nodes of the input graph one by one, in the same way as in classical online algorithms, but for each new node the algorithm can also inspect its radius$T$ neighborhood before choosing the output; instead of looking ahead in time, we have the power of looking around in space. It is natural

The Complexity of Vector Partition arXiv.cs.DS Pub Date : 20210914
Shmuel OnnWe consider the {\em vector partition problem}, where $n$ agents, each with a $d$dimensional attribute vector, are to be partitioned into $p$ parts so as to minimize cost which is a given function on the sums of attribute vectors in each part. The problem has applications in a variety of areas including clustering, logistics and health care. We consider the complexity and parameterized complexity

Domain Sparsification of Discrete Distributions using Entropic Independence arXiv.cs.DS Pub Date : 20210914
Nima Anari, Michał DerezińskiWe present a framework for speeding up the time it takes to sample from discrete distributions $\mu$ defined over subsets of size $k$ of a ground set of $n$ elements, in the regime $k\ll n$. We show that having estimates of marginals $\mathbb{P}_{S\sim \mu}[i\in S]$, the task of sampling from $\mu$ can be reduced to sampling from distributions $\nu$ supported on size $k$ subsets of a ground set of

A Dyadic Simulation Approach to Efficient RangeSummability arXiv.cs.DS Pub Date : 20210913
Jingfan Meng, Huayi Wang, Jun Xu, Mitsunori OgiharaEfficient rangesummability (ERS) of a long list of random variables is a fundamental algorithmic problem that has applications to three important database applications, namely, data stream processing, spaceefficient histogram maintenance (SEHM), and approximate nearest neighbor searches (ANNS). In this work, we propose a novel dyadic simulation framework and develop three novel ERS solutions, namely

Computing Balanced Solutions for Large International Kidney Exchange Schemes arXiv.cs.DS Pub Date : 20210914
Márton Benedek, Péter Biró, Walter Kern, Daniël PaulusmaTo overcome incompatibility issues, kidney patients may swap their donors. In international kidney exchange programmes (IKEPs), countries merge their national patientdonor pools. We consider a recent credit system where in each round, countries are given an initial kidney transplant allocation which is adjusted by a credit function yielding a target allocation. The goal is to find a solution in the

Construction of $k$matchings and $k$regular subgraphs in graph products arXiv.cs.DS Pub Date : 20210914
Anna Lindeberg, Marc HellmuthA $k$matching $M$ of a graph $G=(V,E)$ is a subset $M\subseteq E$ such that each connected component in the subgraph $F = (V,M)$ of $G$ is either a singlevertex graph or $k$regular, i.e., each vertex has degree $k$. In this contribution, we are interested in $k$matchings within the four standard graph products: the Cartesian, strong, direct and lexicographic product. As we shall see, the problem

$\varepsilon$isometric dimension reduction for incompressible subsets of $\ell_p$ arXiv.cs.DS Pub Date : 20210914
Alexandros EskenazisFix $p\in[1,\infty)$, $K\in(0,\infty)$ and a probability measure $\mu$. We prove that for every $n\in\mathbb{N}$, $\varepsilon\in(0,1)$ and $x_1,\ldots,x_n\in L_p(\mu)$ with $\big\ \max_{i\in\{1,\ldots,n\}} x_i \big\_{L_p(\mu)} \leq K$, there exists $d\leq \frac{32e^2 (2K)^{2p}\log n}{\varepsilon^2}$ and vectors $y_1,\ldots, y_n \in \ell_p^d$ such that $$\forall \ i,j\in\{1,\ldots,n\}, \qquad

Beyond Distributed Subgraph Detection: Induced Subgraphs, Multicolored Problems and Graph Parameters arXiv.cs.DS Pub Date : 20210914
Janne H. Korhonen, Amir NikabadiSubgraph detection has recently been one of the most studied problems in the CONGEST model of distributed computing. In this work, we study the distributed complexity of problems closely related to subgraph detection, mainly focusing on induced subgraph detection. The main line of this work presents lower bounds and parameterized algorithms w.r.t structural parameters of the input graph:  On general

Serial and parallel kernelization of Multiple Hitting Set parameterized by the Dilworth number, implemented on the GPU arXiv.cs.DS Pub Date : 20210913
René van Bevern, Artem M. Kirilin, Daniel A. Skachkov, Pavel V. Smirnov, Oxana Yu. TsidulkoThe NPhard Multiple Hitting Set problem is finding a minimumcardinality set intersecting each of the sets in a given input collection a given number of times. Generalizing a wellknown data reduction algorithm due to Weihe, we show a problem kernel for Multiple Hitting Set parameterized by the Dilworth number, a graph parameter introduced by Foldes and Hammer in 1978 yet seemingly so far unexplored

Predictable universally unique identification of sequential events on complex objects arXiv.cs.DS Pub Date : 20210913
Davi PereiraSantosInstituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, Gabriel DalfornoInstituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, André C. P. L. F. CarvalhoInstituto de Ciências Matemáticas e de Computação, Universidade de São PauloUniversal identifiers and hashing have been widely adopted in computer science from distributed financial transactions to data science. This is a consequence of their capability to avoid many shortcomings of relative identifiers, such as limited scope and the need for central management. However, the current identifiers in use are isolated entities which cannot provide much information about the relationship

Maximum Matching sans Maximal Matching: A New Approach for Finding Maximum Matchings in the Data Stream Model arXiv.cs.DS Pub Date : 20210913
Moran Feldman, Ariel SzarfThe problem of finding a maximum size matching in a graph (known as the maximum matching problem) is one of the most classical problems in computer science. Despite a significant body of work dedicated to the study of this problem in the data stream model, the stateoftheart singlepass semistreaming algorithm for it is still a simple greedy algorithm that computes a maximal matching, and this way

Decremental AllPairs Shortest Paths in Deterministic NearLinear Time arXiv.cs.DS Pub Date : 20210912
Julia ChuzhoyWe study the decremental AllPairs Shortest Paths (APSP) problem in undirected edgeweighted graphs. The input to the problem is an $n$vertex $m$edge graph $G$ with nonnegative edge lengths, that undergoes a sequence of edge deletions. The goal is to support approximate shortestpath queries: given a pair $x,y$ of vertices of $G$, return a path $P$ connecting $x$ to $y$, whose length is within factor

MaximumProfit Routing Problem with Multiple Vehicles per Site arXiv.cs.DS Pub Date : 20210912
Bogdan ArmaseluWe consider the MaximumProfit Routing Problem (MPRP), a variant of pickup routing problem introduced in \cite{ArmaseluarXiv2016, ArmaseluPETRA}, in which the goal is to maximize total profit. The original MPRP restricts vehicles to visit a site at most once. In this paper, we consider extensions of MPRP, in which a site may be visited by a vehicle multiple times. Specifically, we consider two

The Labeled Direct Product Optimally Solves String Problems on Graphs arXiv.cs.DS Pub Date : 20210911
Nicola Rizzo, Alexandru I. Tomescu, Alberto PolicritiSuffix trees are an important data structure at the core of optimal solutions to many fundamental string problems, such as exact pattern matching, longest common substring, matching statistics, and longest repeated substring. Recent lines of research focused on extending some of these problems to vertexlabeled graphs, although using adhoc approaches which in some cases do not generalize to all input

A Note on ProjectionBased Recovery of Clusters in Markov Chains arXiv.cs.DS Pub Date : 20210911
Sam ColeLet $T_0$ be the transition matrix of a purely clustered Markov chain, i.e. a direct sum of $k \geq 2$ irreducible stochastic matrices. Given a perturbation $T(x) = T_0 + xE$ of $T_0$ such that $T(x)$ is also stochastic, how small must $x$ be in order for us to recover the indices of the direct summands of $T_0$? We give a simple algorithm based on the orthogonal projection matrix onto the left or

Online Influence Maximization with Nodelevel Feedback Using Standard Offline Oracles arXiv.cs.DS Pub Date : 20210913
Zhijie Zhang, Wei Chen, Xiaoming Sun, Jialin ZhangWe study the online influence maximization (OIM) problem in social networks, where in multiple rounds the learner repeatedly chooses seed nodes to generate cascades, observes the cascade feedback, and gradually learns the best seeds that generate the largest cascade. We focus on two major challenges in this paper. First, we work with nodelevel feedback instead of edgelevel feedback. The edgelevel

NimberPreserving Reductions and Homomorphic SpragueGrundy Game Encodings arXiv.cs.DS Pub Date : 20210912
Kyle Burke, Matthew Ferland, Shanghua TengThe concept of nimbersa.k.a. Grundyvalues or nimvaluesis fundamental to combinatorial game theory. Nimbers provide a complete characterization of strategic interactions among impartial games in their disjunctive sums as well as the winnability. In this paper, we initiate a study of nimberpreserving reductions among impartial games. These reductions enhance the winnabilitypreserving reductions

Developing Mathematical Oracle Functions for Grover Quantum Search Algorithm arXiv.cs.DS Pub Date : 20210903
Cesar Borisovich Pronin, Andrey Vladimirovich OstroukhThis article highlights some of the key operating principles of Grover algorithm. These principles were used to develop a new oracle function, that illustrates the possibility of using Grover algorithm for solving more realistic and specific search problems, like searching for a solution to a simple mathematical equation.

Efficient Locally Optimal Number Set Partitioning for Scheduling, Allocation and Fair Selection arXiv.cs.DS Pub Date : 20210910
Kaan Gokcesu, Hakan GokcesuWe study the optimization version of the set partition problem (where the difference between the partition sums are minimized), which has numerous applications in decision theory literature. While the set partitioning problem is NPhard and requires exponential complexity to solve (i.e., intractable); we formulate a weaker version of this NPhard problem, where the goal is to find a locally optimal

CMinHash: Practically Reducing Two Permutations to Just One arXiv.cs.DS Pub Date : 20210910
Xiaoyun Li, Ping LiTraditional minwise hashing (MinHash) requires applying $K$ independent permutations to estimate the Jaccard similarity in massive binary (0/1) data, where $K$ can be (e.g.,) 1024 or even larger, depending on applications. The recent work on CMinHash (Li and Li, 2021) has shown, with rigorous proofs, that only two permutations are needed. An initial permutation is applied to break whatever structures

AllPurpose Hashing arXiv.cs.DS Pub Date : 20210909
Michael A. Bender, Alex Conway, Martín FarachColton, William Kuszmaul, Guido TagliaviniDespite being one of the oldest data structures in computer science, hash tables continue to be the focus of a great deal of both theoretical and empirical research. A central reason for this is that many of the fundamental properties that one desires from a hash table are difficult to achieve simultaneously; thus many variants offering different tradeoffs have been proposed. This paper introduces

Proceedings of the 29th International Symposium on Graph Drawing and Network Visualization (GD 2021) arXiv.cs.DS Pub Date : 20210910
Helen Purchase, Ignaz RutterThis is the arXiv index for the electronic proceedings of GD 2021, which contains the peerreviewed and revised accepted papers with an optional appendix. Proceedings (without appendices) are also to be published by Springer in the Lecture Notes in Computer Science series.

ReLU Regression with Massart Noise arXiv.cs.DS Pub Date : 20210910
Ilias Diakonikolas, Jongho Park, Christos TzamosWe study the fundamental problem of ReLU regression, where the goal is to fit Rectified Linear Units (ReLUs) to data. This supervised learning task is efficiently solvable in the realizable setting, but is known to be computationally hard with adversarial label noise. In this work, we focus on ReLU regression in the Massart noise model, a natural and wellstudied semirandom noise model. In this model

Fast Algorithms for Minimum Cycle Basis and Minimum Homology Basis arXiv.cs.DS Pub Date : 20210909
Abhishek RathodWe study the problem of finding a minimum homology basis, that is, a shortest set of cycles that generates the $1$dimensional homology classes with $\mathbb{Z}_2$ coefficients in a given simplicial complex $K$. This problem has been extensively studied in the last few years. For general complexes, the current best deterministic algorithm, by Dey et al., runs in $O(N^\omega + N^2 g)$ time, where $N$

Featurebased Individual Fairness in kClustering arXiv.cs.DS Pub Date : 20210909
Debajyoti Kar, Sourav Medya, Debmalya Mandal, Arlei Silva, Palash Dey, Swagato SanyalEnsuring fairness in machine learning algorithms is a challenging and important task. We consider the problem of clustering a set of points while ensuring fairness constraints. While there have been several attempts to capture group fairness in the kclustering problem, fairness at an individual level is not wellstudied. We introduce a new notion of individual fairness in kclustering based on features

Improved Online Algorithm for Fractional Knapsack in the Random Order Model arXiv.cs.DS Pub Date : 20210909
Jeff Giliberti, Andreas KarrenbauerThe fractional knapsack problem is one of the classical problems in combinatorial optimization, which is well understood in the offline setting. However, the corresponding online setting has been handled only briefly in the theoretical computer science literature so far, although it appears in several applications. Even the previously best known guarantee for the competitive ratio was worse than the

MultiConstraint Shortest Path using Forest Hop Labeling arXiv.cs.DS Pub Date : 20210909
Ziyi Liu, Lei Li, Mengxuan Zhang, Wen Hua, Xiaofang ZhouThe \textit{MultiConstraint Shortest Path (MCSP)} problem aims to find the shortest path between two nodes in a network subject to a given constraint set. It is typically processed as a \textit{skyline path} problem. However, the number of intermediate skyline paths becomes larger as the network size increases and the constraint number grows, which brings about the dramatical growth of computational

Algorithms and Certificates for Boolean CSP Refutation: "Smoothed is no harder than Random" arXiv.cs.DS Pub Date : 20210909
Venkatesan Guruswami, Pravesh K. Kothari, Peter ManoharWe present an algorithm for strongly refuting smoothed instances of all Boolean CSPs. The smoothed model is a hybrid between worst and averagecase input models, where the input is an arbitrary instance of the CSP with only the negation patterns of the literals rerandomized with some small probability. For an $n$variable smoothed instance of a $k$arity CSP, our algorithm runs in $n^{O(\ell)}$ time

Online Search for a Hyperplane in HighDimensional Euclidean Space arXiv.cs.DS Pub Date : 20210909
Antonios Antoniadis, Ruben Hoeksma, Sándor KisfaludiBak, Kevin SchewiorWe consider the online search problem in which a server starting at the origin of a $d$dimensional Euclidean space has to find an arbitrary hyperplane. The bestpossible competitive ratio and the length of the shortest curve from which each point on the $d$dimensional unit sphere can be seen are within a constant factor of each other. We show that this length is in $\Omega(d)\cap O(d^{3/2})$.

Improved Hardness of BDD and SVP Under Gap(S)ETH arXiv.cs.DS Pub Date : 20210909
Huck Bennett, Chris Peikert, Yi Tang$\newcommand{\Z}{\mathbb{Z}}$ We show improved finegrained hardness of two key lattice problems in the $\ell_p$ norm: Bounded Distance Decoding to within an $\alpha$ factor of the minimum distance ($\mathrm{BDD}_{p, \alpha}$) and the (decisional) $\gamma$approximate Shortest Vector Problem ($\mathrm{SVP}_{p,\gamma}$), assuming variants of the Gap (Strong) Exponential Time Hypothesis (Gap(S)ETH)

Adversarially Robust Streaming via DenseSparse Tradeoffs arXiv.cs.DS Pub Date : 20210908
Omri BenEliezer, Talya Eden, Krzysztof OnakA streaming algorithm is adversarially robust if it is guaranteed to perform correctly even in the presence of an adaptive adversary. Recently, several sophisticated frameworks for robustification of classical streaming algorithms have been developed. One of the main open questions in this area is whether efficient adversarially robust algorithms exist for moment estimation problems under the turnstile

Approximately counting independent sets in bipartite graphs via graph containers arXiv.cs.DS Pub Date : 20210908
Matthew Jenssen, Will Perkins, Aditya PotukuchiBy implementing algorithmic versions of Sapozhenko's graph container methods, we give new algorithms for approximating the number of independent sets in bipartite graphs. Our first algorithm applies to $d$regular, bipartite graphs satisfying a weak expansion condition: when $d$ is constant, and the graph is a bipartite $\Omega( \log^2 d/d)$expander, we obtain an FPTAS for the number of independent

Simple WorstCase Optimal Adaptive PrefixFree Coding arXiv.cs.DS Pub Date : 20210907
Travis GagieGagie and Nekrich (2009) gave an algorithm for adaptive prefixfree coding that, given a string $S [1..n]$ over the alphabet $\{1, \ldots, \sigma\}$ with $\sigma = o (n / \log^{5 / 2} n)$, encodes $S$ in at most $n (H + 1) + o (n)$ bits, where $H$ is the empirical entropy of $S$, such that encoding and decoding $S$ take $O (n)$ time. They also proved their bound on the encoding length is optimal, even

Impatient PPSZ  a Faster algorithm for CSP arXiv.cs.DS Pub Date : 20210907
Shibo Li, Dominik SchederPPSZ is the fastest known algorithm for (d,k)CSP problems, for most values of d and k. It goes through the variables in random order and sets each variable randomly to one of the d colors, excluding those colors that can be ruled out by looking at few constraints at a time. We propose and analyze a modification of PPSZ: whenever all but 2 colors can be ruled out for some variable, immediately set

CongruencyConstrained TU Problems Beyond the Bimodular Case arXiv.cs.DS Pub Date : 20210907
Martin Nägele, Richard Santiago, Rico ZenklusenA longstanding open question in Integer Programming is whether integer programs with constraint matrices with bounded subdeterminants are efficiently solvable. An important special case thereof are congruencyconstrained integer programs $\min\{c^\top x\colon Tx\leq b, \gamma^\top x\equiv r\pmod*{m}, x\in\mathbb{Z}^n\}$ with a totally unimodular constraint matrix $T$. Such problems have been shown

Efficient diagonalization of symmetric matrices associated with graphs of small treewidth arXiv.cs.DS Pub Date : 20210906
Martin Fürer, Carlos Hoppen, Vilmar TrevisanLet $M=(m_{ij})$ be a symmetric matrix of order $n$ whose elements lie in an arbitrary field $\mathbb{F}$, and let $G$ be the graph with vertex set $\{1,\ldots,n\}$ such that distinct vertices $i$ and $j$ are adjacent if and only if $m_{ij} \neq 0$. We introduce a dynamic programming algorithm that finds a diagonal matrix that is congruent to $M$. If $G$ is given with a tree decomposition $\mathcal{T}$

On the query complexity of connectivity with global queries arXiv.cs.DS Pub Date : 20210905
Arinta Auza, Troy LeeWe study the query complexity of determining if a graph is connected with global queries. The first model we look at is matrixvector multiplication queries to the adjacency matrix. Here, for an $n$vertex graph with adjacency matrix $A$, one can query a vector $x \in \{0,1\}^n$ and receive the answer $Ax$. We give a randomized algorithm that can output a spanning forest of a weighted graph with constant

Stretching Your Data With Taffy Filters arXiv.cs.DS Pub Date : 20210904
Jim ApplePopular approximate membership query structures such as Bloom filters and cuckoo filters are widely used in databases, security, and networking. These structures support two operations  insert and lookup; lookup always returns true on elements inserted into the structure, while it returns true with some probability $\varepsilon \ll 1$ on elements not inserted into the structure. These latter elements

Fast Succinct Retrieval and Approximate Membership using Ribbon arXiv.cs.DS Pub Date : 20210904
Peter C. Dillinger, Lorenz HübschleSchneider, Peter Sanders, Stefan WalzerA retrieval data structure for a static function $f:S\rightarrow \{0,1\}^r$ supports queries that return $f(x)$ for any $x \in S$. Retrieval data structures can be used to implement a static approximate membership query data structure (AMQ) (i.e., a Bloom filter alternative) with false positive rate $2^{r}$. The informationtheoretic lower bound for both tasks is $rS$ bits. While succinct theoretical

Improving The FloydWarshall All Pairs Shortest Paths Algorithm arXiv.cs.DS Pub Date : 20210904
Ismail H. TorosluThe FloydWarshall algorithm is the most popular algorithm for determining the shortest paths between all pairs in a graph. It is very a simple and an elegant algorithm. However, if the graph does not contain any negative weighted edge, using Dijkstra's shortest path algorithm for every vertex as a source vertex to produce all pairs shortest paths of the graph works much better than the FloydWarshall

RAMA: A Rapid Multicut Algorithm on GPU arXiv.cs.DS Pub Date : 20210904
Ahmed Abbas, Paul SwobodaWe propose a highly parallel primaldual algorithm for the multicut (a.k.a. correlation clustering) problem, a classical graph clustering problem widely used in machine learning and computer vision. Our algorithm consists of three steps executed recursively: (1) Finding conflicted cycles that correspond to violated inequalities of the underlying multicut relaxation, (2) Performing message passing between

Symmetric Norm Estimation and Regression on Sliding Windows arXiv.cs.DS Pub Date : 20210903
Vladimir Braverman, Viska Wei, Samson ZhouThe sliding window model generalizes the standard streaming model and often performs better in applications where recent data is more important or more accurate than data that arrived prior to a certain time. We study the problem of approximating symmetric norms (a norm on $\mathbb{R}^n$ that is invariant under signflips and coordinatewise permutations) in the sliding window model, where only the

Finding Colorful Paths in Temporal Graphs arXiv.cs.DS Pub Date : 20210903
Riccardo Dondi, Mohammad Mehdi HosseinzadehThe problem of finding paths in temporal graphs has been recently considered due to its many applications. In this paper we consider a variant of the problem that, given a vertexcolored temporal graph, asks for a path whose vertices have distinct colors and include the maximum number of colors. We study the approximation complexity of the problem and we provide an inapproximability lower bound. Then

Improved Approximation Schemes for Dominating Set Problems in Unit Disk Graphs arXiv.cs.DS Pub Date : 20210903
Jittat Fakcharoenphol, Pattara SukprasertWe present two (exponentially) faster PTAS's for dominating set problems in unit disk graphs. Given a geometric representation of a unit disk graph, our PTAS's that find $(1+\epsilon)$approximate solutions to the Minimum Dominating Set (MDS) and the Minimum Connected Dominating Set (MCDS) of the input graph in time $n^{O(1/\epsilon)}$. This can be compared to the best known $n^{O(1/\epsilon \log

ParetoOptimal LearningAugmented Algorithms for Online Conversion Problems arXiv.cs.DS Pub Date : 20210903
Bo Sun, Russell Lee, Mohammad Hajiesmaili, Adam Wierman, Danny H. K. TsangThis paper leverages machinelearned predictions to design competitive algorithms for online conversion problems with the goal of improving the competitive ratio when predictions are accurate (i.e., consistency), while also guaranteeing a worstcase competitive ratio regardless of the prediction quality (i.e., robustness). We unify the algorithmic design of both integral and fractional conversion problems

Computing Graph Descriptors on Edge Streams arXiv.cs.DS Pub Date : 20210902
Zohair Raza Hassan, Imdadullah Khan, Mudassir Shabbir, Waseem AbbasGraph feature extraction is a fundamental task in graphs analytics. Using feature vectors (graph descriptors) in tandem with data mining algorithms that operate on Euclidean data, one can solve problems such as classification, clustering, and anomaly detection on graphstructured data. This idea has proved fruitful in the past, with spectralbased graph descriptors providing stateoftheart classification

Optimization and Sampling Under Continuous Symmetry: Examples and Lie Theory arXiv.cs.DS Pub Date : 20210902
Jonathan Leake, Nisheeth K. VishnoiIn the last few years, the notion of symmetry has provided a powerful and essential lens to view several optimization or sampling problems that arise in areas such as theoretical computer science, statistics, machine learning, quantum inference, and privacy. Here, we present two examples of nonconvex problems in optimization and sampling where continuous symmetries play  implicitly or explicitly

Some Inapproximability Results of MAP Inference and Exponentiated Determinantal Point Processes arXiv.cs.DS Pub Date : 20210902
Naoto OhsakaWe study the computational complexity of two hard problems on determinantal point processes (DPPs). One is maximum a posteriori (MAP) inference, i.e., to find a principal submatrix having the maximum determinant. The other is probabilistic inference on exponentiated DPPs (EDPPs), which can sharpen or weaken the diversity preference of DPPs with an exponent parameter $p$. We prove the following complexitytheoretic