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The Fine-Grained Complexity of Graph Homomorphism Parameterized by Clique-Width ACM Trans. Algorithms (IF 1.3) Pub Date : 2024-03-25 Robert Ganian, Thekla Hamm, Viktoriia Korchemna, Karolina Okrasa, Kirill Simonov
The generic homomorphism problem, which asks whether an input graph \(G\) admits a homomorphism into a fixed target graph \(H\), has been widely studied in the literature. In this article, we provide a fine-grained complexity classification of the running time of the homomorphism problem with respect to the clique-width of \(G\) (denoted \({\operatorname{cw}}\)) for virtually all choices of \(H\) under
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Isomorphism Testing for Graphs Excluding Small Topological Subgraphs ACM Trans. Algorithms (IF 1.3) Pub Date : 2024-03-13 Daniel Neuen
We give an isomorphism test that runs in time \(n^{\operatorname{polylog}(h)} \) on all n-vertex graphs excluding some h-vertex graph as a topological subgraph. Previous results state that isomorphism for such graphs can be tested in time \(n^{\operatorname{polylog}(n)} \) (Babai, STOC 2016) and nf(h) for some function f (Grohe and Marx, SIAM J. Comp., 2015). Our result also unifies and extends previous
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Width Helps and Hinders Splitting Flows ACM Trans. Algorithms (IF 1.3) Pub Date : 2024-03-13 Manuel Cáceres, Massimo Cairo, Andreas Grigorjew, Shahbaz Khan, Brendan Mumey, Romeo Rizzi, Alexandru I. Tomescu, Lucia Williams
Minimum flow decomposition (MFD) is the NP-hard problem of finding a smallest decomposition of a network flow/circulation X on a directed graph G into weighted source-to-sink paths whose weighted sum equals X. We show that, for acyclic graphs, considering the width of the graph (the minimum number of paths needed to cover all of its edges) yields advances in our understanding of its approximability
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Flow-augmentation II: Undirected Graphs ACM Trans. Algorithms (IF 1.3) Pub Date : 2024-03-13 Eun Jung Kim, Stefan Kratsch, Marcin Pilipczuk, Magnus Wahlström
We present an undirected version of the recently introduced flow-augmentation technique: Given an undirected multigraph G with distinguished vertices s,t ∈ V(G) and an integer k, one can in randomized k𝒪(1) ⋅ (|V(G)| + |E(G)|) time sample a set A ⊆ \(\binom{V(G)}{2}\) such that the following holds: for every inclusion-wise minimal st-cut Z in G of cardinality at most k, Z becomes a minimum-cardinality
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Map Matching Queries on Realistic Input Graphs Under the Fréchet Distance ACM Trans. Algorithms (IF 1.3) Pub Date : 2024-03-13 Joachim Gudmundsson, Martin P. Seybold, Sampson Wong
Map matching is a common preprocessing step for analysing vehicle trajectories. In the theory community, the most popular approach for map matching is to compute a path on the road network that is the most spatially similar to the trajectory, where spatial similarity is measured using the Fréchet distance. A shortcoming of existing map matching algorithms under the Fréchet distance is that every time
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The Complexity of Finding Fair Many-to-One Matchings ACM Trans. Algorithms (IF 1.3) Pub Date : 2024-02-24 Niclas Boehmer, Tomohiro Koana
We analyze the (parameterized) computational complexity of “fair” variants of bipartite many-to-one matching, where each vertex from the “left” side is matched to exactly one vertex and each vertex from the “right” side may be matched to multiple vertices. We want to find a “fair” matching, in which each vertex from the right side is matched to a “fair” set of vertices. Assuming that each vertex from
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On the Two-Dimensional Knapsack Problem for Convex Polygons ACM Trans. Algorithms (IF 1.3) Pub Date : 2024-02-20 Arturo Merino, Andreas Wiese
We study the two-dimensional geometric knapsack problem for convex polygons. Given a set of weighted convex polygons and a square knapsack, the goal is to select the most profitable subset of the given polygons that fits non-overlappingly into the knapsack. We allow to rotate the polygons by arbitrary angles. We present a quasi-polynomial time O(1)-approximation algorithm for the general case and a
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Contraction Decomposition in Unit Disk Graphs and Algorithmic Applications in Parameterized Complexity ACM Trans. Algorithms (IF 1.3) Pub Date : 2024-02-15 Fahad Panolan, Saket Saurabh, Meirav Zehavi
We give a new decomposition theorem in unit disk graphs (UDGs) and demonstrate its applicability in the fields of Structural Graph Theory and Parameterized Complexity. First, our new decomposition theorem shows that the class of UDGs admits an “almost” Contraction Decomposition Theorem. Prior studies on this topic exhibited that the classes of planar graphs [Klein, SICOMP, 2008], graphs of bounded
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Counting List Homomorphisms from Graphs of Bounded Treewidth: Tight Complexity Bounds ACM Trans. Algorithms (IF 1.3) Pub Date : 2024-02-13 Jacob Focke, Dániel Marx, Paweł Rzążewski
The goal of this work is to give precise bounds on the counting complexity of a family of generalized coloring problems (list homomorphisms) on bounded-treewidth graphs. Given graphs G, H, and lists \(L(v)\subseteq V(H)\) for every \(v\in V(G)\), a list homomorphism is a function \(f:V(G)\rightarrow V(H)\) that preserves the edges (i.e., \(uv\in E(G)\) implies \(f(u)f(v)\in E(H)\)) and respects the
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Generic Non-Recursive Suffix Array Construction ACM Trans. Algorithms (IF 1.3) Pub Date : 2024-02-08 Jannik Olbrich, Enno Ohlebusch, Thomas Büchler
The suffix array is arguably one of the most important data structures in sequence analysis and consequently there is a multitude of suffix sorting algorithms. However, to this date the GSACA algorithm introduced in 2015 is the only known non-recursive linear-time suffix array construction algorithm (SACA). Despite its interesting theoretical properties, there has been little effort in improving GSACA’s
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Ultrasparse Ultrasparsifiers and Faster Laplacian System Solvers ACM Trans. Algorithms (IF 1.3) Pub Date : 2024-02-02 Arun Jambulapati, Aaron Sidford
In this paper we provide an O(mloglogO(1)nlog (1/ϵ))-expected time algorithm for solving Laplacian systems on n-node m-edge graphs, improving upon the previous best expected runtime of \(O(m \sqrt {\log n} \mathrm{log log}^{O(1)} n \log (1/\epsilon)) \) achieved by (Cohen, Kyng, Miller, Pachocki, Peng, Rao, Xu 2014). To obtain this result we provide efficient constructions of low spectral stretch graph
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On the External Validity of Average-case Analyses of Graph Algorithms ACM Trans. Algorithms (IF 1.3) Pub Date : 2024-01-22 Thomas Bläsius, Philipp Fischbeck
The number one criticism of average-case analysis is that we do not actually know the probability distribution of real-world inputs. Thus, analyzing an algorithm on some random model has no implications for practical performance. At its core, this criticism doubts the existence of external validity; i.e., it assumes that algorithmic behavior on the somewhat simple and clean models does not translate
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Fast Sampling via Spectral Independence Beyond Bounded-degree Graphs ACM Trans. Algorithms (IF 1.3) Pub Date : 2024-01-22 Ivona Bezáková, Andreas Galanis, Leslie Ann Goldberg, Daniel Štefankovič
Spectral independence is a recently developed framework for obtaining sharp bounds on the convergence time of the classical Glauber dynamics. This new framework has yielded optimal O(n log n) sampling algorithms on bounded-degree graphs for a large class of problems throughout the so-called uniqueness regime, including, for example, the problems of sampling independent sets, matchings, and Ising-model
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Popular Matchings with One-Sided Bias ACM Trans. Algorithms (IF 1.3) Pub Date : 2023-12-27 Telikepalli Kavitha
Let G = (A∪B, E) be a bipartite graph where the set A consists of agents or main players and the set B consists of jobs or secondary players. Every vertex in A∪B has a strict ranking of its neighbors. A matching M is popular if for any matching N, the number of vertices that prefer M to N is at least the number that prefer N to M. Popular matchings always exist in G since every stable matching is popular
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Optimal Inapproximability with Universal Factor Graphs ACM Trans. Algorithms (IF 1.3) Pub Date : 2023-12-15 Per Austrin, Jonah Brown-Cohen, Johan Håstad
The factor graph of an instance of a constraint satisfaction problem (CSP) is the bipartite graph indicating which variables appear in each constraint. An instance of the CSP is given by the factor graph together with a list of which predicate is applied for each constraint. We establish that many Max-CSPs remain as hard to approximate as in the general case even when the factor graph is fixed (depending
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Cluster Editing Parameterized above Modification-disjoint P3-packings ACM Trans. Algorithms (IF 1.3) Pub Date : 2023-12-10 Shaohua Li, Marcin Pilipczuk, Manuel Sorge
Given a graph G =(V,E) and an integer k, the Cluster Editing problem asks whether we can transform G into a union of vertex-disjoint cliques by at most k modifications (edge deletions or insertions). In this paper, we study the following variant of Cluster Editing. We are given a graph G = (V,E), a packing ℋ of modification-disjoint induced P3s (no pair of P3s in ℋ share an edge or non-edge) and an
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Genome Assembly, from Practice to Theory: Safe, Complete and Linear-Time ACM Trans. Algorithms (IF 1.3) Pub Date : 2023-12-10 Massimo Cairo, Romeo Rizzi, Alexandru I. Tomescu, Elia C. Zirondelli
Genome assembly asks to reconstruct an unknown string from many shorter substrings of it. Even though it is one of the key problems in Bioinformatics, it is generally lacking major theoretical advances. Its hardness stems both from practical issues (size and errors of real data), and from the fact that problem formulations inherently admit multiple solutions. Given these, at their core, most state-of-the-art
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Approximating Sparsest Cut in Low-Treewidth Graphs via Combinatorial Diameter ACM Trans. Algorithms (IF 1.3) Pub Date : 2023-11-14 Parinya Chalermsook, Matthias Kaul, Matthias Mnich, Joachim Spoerhase, Sumedha Uniyal, Daniel Vaz
The fundamental Sparsest Cut problem takes as input a graph G together with edge capacities and demands, and seeks a cut that minimizes the ratio between the capacities and demands across the cuts. For n-vertex graphs G of treewidth k, Chlamtáč, Krauthgamer, and Raghavendra (APPROX 2010) presented an algorithm that yields a factor-\(2^{2^k} \) approximation in time 2O(k) · nO(1). Later, Gupta, Talwar
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Additive Sparsification of CSPs ACM Trans. Algorithms (IF 1.3) Pub Date : 2023-11-13 Eden Pelleg, Stanislav Živný
Multiplicative cut sparsifiers, introduced by Benczúr and Karger [STOC’96], have proved extremely influential and found various applications. Precise characterisations were established for sparsifiability of graphs with other 2-variable predicates on Boolean domains by Filtser and Krauthgamer [SIDMA’17] and non-Boolean domains by Butti and Živný [SIDMA’20]. Bansal, Svensson and Trevisan [FOCS’19] introduced
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Shortest Cycles with Monotone Submodular Costs ACM Trans. Algorithms (IF 1.3) Pub Date : 2023-11-13 Fedor V. Fomin, Petr A. Golovach, Tuukka Korhonen, Daniel Lokshtanov, Giannos Stamoulis
We introduce the following submodular generalization of the Shortest Cycle problem. For a nonnegative monotone submodular cost function f defined on the edges (or the vertices) of an undirected graph G, we seek for a cycle C in G of minimum cost 𝖮𝖯𝖳 = f(C). We give an algorithm that given an n-vertex graph G, parameter ɛ > 0, and the function f represented by an oracle, in time n𝒪(log 1/ɛ) finds
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Fast and perfect sampling of subgraphs and polymer systems ACM Trans. Algorithms (IF 1.3) Pub Date : 2023-11-10 Antonio Blanca, Sarah Cannon, Will Perkins
We give an efficient perfect sampling algorithm for weighted, connected induced subgraphs (or graphlets) of rooted, bounded degree graphs. Our algorithm utilizes a vertex-percolation process with a carefully chosen rejection filter and works under a percolation subcriticality condition. We show that this condition is optimal in the sense that the task of (approximately) sampling weighted rooted graphlets
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Static and Streaming Data Structures for Fréchet Distance Queries ACM Trans. Algorithms (IF 1.3) Pub Date : 2023-10-25 Arnold Filtser, Omrit Filtser
Given a curve P with points in ℝd in a streaming fashion, and parameters ɛ > 0 and k, we construct a distance oracle that uses \(O(\frac{1}{\varepsilon })^{kd}\log \varepsilon ^{-1}\) space, and given a query curve Q with k points in ℝd returns in \(\tilde{O}(kd)\) time a 1+ɛ approximation of the discrete Fréchet distance between Q and P. In addition, we construct simplifications in the streaming model
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An Improved Algorithm for The k-Dyck Edit Distance Problem ACM Trans. Algorithms (IF 1.3) Pub Date : 2023-10-19 Dvir Fried, Shay Golan, Tomasz Kociumaka, Tsvi Kopelowitz, Ely Porat, Tatiana Starikovskaya
A Dyck sequence is a sequence of opening and closing parentheses (of various types) that is balanced. The Dyck edit distance of a given sequence of parentheses S is the smallest number of edit operations (insertions, deletions, and substitutions) needed to transform S into a Dyck sequence. We consider the threshold Dyck edit distance problem, where the input is a sequence of parentheses S and a positive
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A Cubic Algorithm for Computing the Hermite Normal Form of a Nonsingular Integer Matrix ACM Trans. Algorithms (IF 1.3) Pub Date : 2023-10-14 Stavros Birmpilis, George Labahn, Arne Storjohann
A Las Vegas randomized algorithm is given to compute the Hermite normal form of a nonsingular integer matrix A of dimension n. The algorithm uses quadratic integer multiplication and cubic matrix multiplication and has running time bounded by O(n3 (log n + log ||A||)2(log n)2) bit operations, where ||A||= max ij |Aij| denotes the largest entry of A in absolute value. A variant of the algorithm that
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Minimum+1 (s, t)-cuts and Dual-edge Sensitivity Oracle ACM Trans. Algorithms (IF 1.3) Pub Date : 2023-10-14 Surender Baswana, Koustav Bhanja, Abhyuday Pandey
Let G be a directed multi-graph on n vertices and m edges with a designated source vertex s and a designated sink vertex t. We study the (s,t)-cuts of capacity minimum+1 and as an important application of them, we give a solution to the dual-edge sensitivity for (s,t)-mincuts—reporting an (s,t)-mincut upon failure or insertion of any pair of edges. Picard and Queyranne [Mathematical Programming Studies
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Scalable High-Quality Hypergraph Partitioning ACM Trans. Algorithms (IF 1.3) Pub Date : 2023-10-09 Lars Gottesbüren, Tobias Heuer, Nikolai Maas, Peter Sanders, Sebastian Schlag
Balanced hypergraph partitioning is an NP-hard problem with many applications, e.g., optimizing communication in distributed data placement problems. The goal is to place all nodes across k different blocks of bounded size, such that hyperedges span as few parts as possible. This problem is well-studied in sequential and distributed settings, but not in shared-memory. We close this gap by devising
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Approximating Nash Social Welfare under Submodular Valuations through (Un)Matchings ACM Trans. Algorithms (IF 1.3) Pub Date : 2023-09-26 Jugal Garg, Pooja Kulkarni, Rucha Kulkarni
We study the problem of approximating maximum Nash social welfare (NSW) when allocating m indivisible items among n asymmetric agents with submodular valuations. The NSW is a well-established notion of fairness and efficiency, defined as the weighted geometric mean of agents’ valuations. For special cases of the problem with symmetric agents and additive(-like) valuation functions, approximation algorithms
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String Indexing with Compressed Patterns ACM Trans. Algorithms (IF 1.3) Pub Date : 2023-09-26 Philip Bille, Inge Li Gørtz, Teresa Anna Steiner
Given a string S of length n, the classic string indexing problem is to preprocess S into a compact data structure that supports efficient subsequent pattern queries. In this article, we consider the basic variant where the pattern is given in compressed form and the goal is to achieve query time that is fast in terms of the compressed size of the pattern. This captures the common client-server scenario
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Near-Optimal Time–Energy Tradeoffs for Deterministic Leader Election ACM Trans. Algorithms (IF 1.3) Pub Date : 2023-09-26 Yi-Jun Chang, Ran Duan, Shunhua Jiang
We consider the energy complexity of the leader election problem in the single-hop radio network model, where each device v has a unique identifier ID(v) ∈{ 1, 2, ⋖ , N} . Energy is a scarce resource for small battery-powered devices. For such devices, most of the energy is often spent on communication, not on computation. To approximate the actual energy cost, the energy complexity of an algorithm
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Synchronized Planarity with Applications to Constrained Planarity Problems ACM Trans. Algorithms (IF 1.3) Pub Date : 2023-09-26 Thomas Bläsius, Simon D. Fink, Ignaz Rutter
We introduce the problem Synchronized Planarity. Roughly speaking, its input is a loop-free multi-graph together with synchronization constraints that, e.g., match pairs of vertices of equal degree by providing a bijection between their edges. Synchronized Planarity then asks whether the graph admits a crossing-free embedding into the plane such that the orders of edges around synchronized vertices
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Recognizing k-Leaf Powers in Polynomial Time, for Constant k ACM Trans. Algorithms (IF 1.3) Pub Date : 2023-09-26 Manuel Lafond
A graph G is a k-leaf power if there exists a tree T whose leaf set is V(G), and such that uv ∈ E(G) if and only if the distance between u and v in T is at most k (and u ≠ v). The graph classes of k-leaf powers have several applications in computational biology, but recognizing them has remained a challenging algorithmic problem for the past two decades. The best known result is that 6-leaf powers
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A Polynomial-Time Algorithm for 1/3-Approximate Nash Equilibria in Bimatrix Games ACM Trans. Algorithms (IF 1.3) Pub Date : 2023-08-08 Argyrios Deligkas, Michail Fasoulakis, Evangelos Markakis
Since the celebrated PPAD-completeness result for Nash equilibria in bimatrix games, a long line of research has focused on polynomial-time algorithms that compute ε-approximate Nash equilibria. Finding the best possible approximation guarantee that we can have in polynomial time has been a fundamental and non-trivial pursuit on settling the complexity of approximate equilibria. Despite a significant
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Static and Streaming Data Structures for Fréchet Distance Queries ACM Trans. Algorithms (IF 1.3) Pub Date : 2023-07-24 Arnold Filtser, Omrit Filtser
Given a curve P with points in \(\mathbb {R}^d \) in a streaming fashion, and parameters ε > 0 and k, we construct a distance oracle that uses \(O(\frac{1}{\varepsilon })^{kd}\log \varepsilon ^{-1} \) space, and given a query curve Q with k points in \(\mathbb {R}^d \), returns in \(\tilde{O}(kd) \) time a 1 + ε approximation of the discrete Fréchet distance between Q and P. In addition, we construct
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String Indexing with Compressed Patterns ACM Trans. Algorithms (IF 1.3) Pub Date : 2023-07-21 Philip Bille, Inge Li Gørtz, Teresa Anna Steiner
Given a string S of length n, the classic string indexing problem is to preprocess S into a compact data structure that supports efficient subsequent pattern queries. In this paper we consider the basic variant where the pattern is given in compressed form and the goal is to achieve query time that is fast in terms of the compressed size of the pattern. This captures the common client-server scenario
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Matching on the Line Admits no \(o(\sqrt {\log n})\) -Competitive Algorithm ACM Trans. Algorithms (IF 1.3) Pub Date : 2023-07-14 Enoch Peserico, Michele Scquizzato
We present a simple proof that no randomized online matching algorithm for the line can be \((\sqrt {\log _2(n+1)}/15)\)-competitive against an oblivious adversary for any n = 2i - 1 : i ∈ ℕ. This is the first super-constant lower bound for the problem, and disproves as a corollary a recent conjecture on the topology-parametrized competitiveness achievable on generic spaces.
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Fréchet Distance for Uncertain Curves ACM Trans. Algorithms (IF 1.3) Pub Date : 2023-07-14 Kevin Buchin, Chenglin Fan, Maarten Löffler, Aleksandr Popov, Benjamin Raichel, Marcel Roeloffzen
In this article, we study a wide range of variants for computing the (discrete and continuous) Fréchet distance between uncertain curves. An uncertain curve is a sequence of uncertainty regions, where each region is a disk, a line segment, or a set of points. A realisation of a curve is a polyline connecting one point from each region. Given an uncertain curve and a second (certain or uncertain) curve
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Tiling with Squares and Packing Dominos in Polynomial Time ACM Trans. Algorithms (IF 1.3) Pub Date : 2023-07-14 Anders Aamand, Mikkel Abrahamsen, Peter M. R. Rasmussen, Thomas D. Ahle
A polyomino is a polygonal region with axis-parallel edges and corners of integral coordinates, which may have holes. In this paper, we consider planar tiling and packing problems with polyomino pieces and a polyomino container P. We give polynomial-time algorithms for deciding if P can be tiled with k × k squares for any fixed k which can be part of the input (that is, deciding if P is the union of
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A Polynomial-Time Algorithm for 1/3-Approximate Nash Equilibria in Bimatrix Games ACM Trans. Algorithms (IF 1.3) Pub Date : 2023-07-08 Argyrios Deligkas, Michail Fasoulakis, Evangelos Markakis
Since the celebrated PPAD-completeness result for Nash equilibria in bimatrix games, a long line of research has focused on polynomial-time algorithms that compute ε-approximate Nash equilibria. Finding the best possible approximation guarantee that we can have in polynomial time has been a fundamental and non-trivial pursuit on settling the complexity of approximate equilibria. Despite a significant
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Competitive Online Search Trees on Trees ACM Trans. Algorithms (IF 1.3) Pub Date : 2023-06-24 Prosenjit Bose, Jean Cardinal, John Iacono, Grigorios Koumoutsos, Stefan Langerman
We consider the design of adaptive data structures for searching elements of a tree-structured space. We use a natural generalization of the rotation-based online binary search tree model in which the underlying search space is the set of vertices of a tree. This model is based on a simple structure for decomposing graphs, previously known under several names including elimination trees, vertex rankings
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Efficient and Near-optimal Algorithms for Sampling Small Connected Subgraphs ACM Trans. Algorithms (IF 1.3) Pub Date : 2023-06-24 Marco Bressan
We study the following problem: Given an integer k ≥ 3 and a simple graph G, sample a connected induced k-vertex subgraph of G uniformly at random. This is a fundamental graph mining primitive with applications in social network analysis, bioinformatics, and more. Surprisingly, no efficient algorithm is known for uniform sampling; the only somewhat efficient algorithms available yield samples that
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Towards Optimal Moment Estimation in Streaming and Distributed Models ACM Trans. Algorithms (IF 1.3) Pub Date : 2023-06-24 Rajesh Jayaram, David P. Woodruff
One of the oldest problems in the data stream model is to approximate the pth moment \(\Vert \mathbf {X}\Vert _p^p = \sum _{i=1}^n \mathbf {X}_i^p\) of an underlying non-negative vector \(\mathbf {X}\in \mathbb {R}^n\), which is presented as a sequence of \(\mathrm{poly}(n)\) updates to its coordinates. Of particular interest is when \(p \in (0,2]\). Although a tight space bound of \(\Theta (\epsilon
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Collapsing the Tower - On the Complexity of Multistage Stochastic IPs ACM Trans. Algorithms (IF 1.3) Pub Date : 2023-06-17 Kim-Manuel Klein, Janina Reuter
In this paper we study the computational complexity of solving a class of block structured integer programs (IPs) - so called multistage stochastic IPs. A multistage stochastic IP is an IP of the form min {c⊺x∣Ax = b, x ≥ 0, x integral} where the constraint matrix A consists of small block matrices ordered on the diagonal line and for each stage there are larger blocks with few columns connecting the
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Almost-Optimal Deterministic Treasure Hunt in Unweighted Graphs ACM Trans. Algorithms (IF 1.3) Pub Date : 2023-05-05 Sébastien Bouchard, Yoann Dieudonné, Arnaud Labourel, Andrzej Pelc
A mobile agent navigating along edges of a simple connected unweighted graph, either finite or countably infinite, has to find an inert target (treasure) hidden in one of the nodes. This task is known as treasure hunt. The agent has no a priori knowledge of the graph, of the location of the treasure, or of the initial distance to it. The cost of a treasure hunt algorithm is the worst-case number of
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Hitting Topological Minor Models in Planar Graphs is Fixed Parameter Tractable ACM Trans. Algorithms (IF 1.3) Pub Date : 2023-05-05 Petr A. Golovach, Giannos Stamoulis, Dimitrios M. Thilikos
For a finite collection of graphs ℱ, the ℱ-TM-Deletion problem has as input an n-vertex graph G and an integer k and asks whether there exists a set S ⊆ V(G) with |S| ≤ k such that G \ S does not contain any of the graphs in ℱ as a topological minor. We prove that for every such ℱ, ℱ -TM-Deletion is fixed parameter tractable on planar graphs. Our algorithm runs in a 2𝒪(k2) ⋅ n2 time, or, alternatively
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Load Thresholds for Cuckoo Hashing with Overlapping Blocks ACM Trans. Algorithms (IF 1.3) Pub Date : 2023-05-05 Stefan Walzer
We consider a natural variation of cuckoo hashing proposed by Lehman and Panigrahy (2009). Each of cn objects is assigned k = 2 intervals of size ℓ in a linear hash table of size n and both starting points are chosen independently and uniformly at random. Each object must be placed into a table cell within its intervals, but each cell can only hold one object. Experiments suggested that this scheme
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On the Complexity of String Matching for Graphs ACM Trans. Algorithms (IF 1.3) Pub Date : 2023-04-12 Massimo Equi, Veli Mäkinen, Alexandru I. Tomescu, Roberto Grossi
Exact string matching in labeled graphs is the problem of searching paths of a graph G=(V, E) such that the concatenation of their node labels is equal to a given pattern string P[1.m]. This basic problem can be found at the heart of more complex operations on variation graphs in computational biology, of query operations in graph databases, and of analysis operations in heterogeneous networks. We
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Hopcroft’s Problem, Log-Star Shaving, 2D Fractional Cascading, and Decision Trees ACM Trans. Algorithms (IF 1.3) Pub Date : 2023-04-11 Timothy M. Chan, Da Wei Zheng
We revisit Hopcroft’s problem and related fundamental problems about geometric range searching. Given n points and n lines in the plane, we show how to count the number of point-line incidence pairs or the number of point-above-line pairs in O(n4/3) time, which matches the conjectured lower bound and improves the best previous time bound of \(n^{4/3}2^{O(\log ^*n)} \) obtained almost 30 years ago by
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Greedy Spanners in Euclidean Spaces Admit Sublinear Separators ACM Trans. Algorithms (IF 1.3) Pub Date : 2023-04-03 Hung Le, Cuong Than
The greedy spanner in a low dimensional Euclidean space is a fundamental geometric construction that has been extensively studied over three decades as it possesses the two most basic properties of a good spanner: constant maximum degree and constant lightness. Recently, Eppstein and Khodabandeh [28] showed that the greedy spanner in \(\mathbb {R}^2 \) admits a sublinear separator in a strong sense:
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PTAS for Sparse General-valued CSPs ACM Trans. Algorithms (IF 1.3) Pub Date : 2023-03-09 Balázs F. Mezei, Marcin Wrochna, stanislav Živný
We study polynomial-time approximation schemes (PTASes) for constraint satisfaction problems (CSPs) such as Maximum Independent Set or Minimum Vertex Cover on sparse graph classes. Baker’s approach gives a PTAS on planar graphs, excluded-minor classes, and beyond. For Max-CSPs, and even more generally, maximisation finite-valued CSPs (where constraints are arbitrary non-negative functions), Romero
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Approximating Pathwidth for Graphs of Small Treewidth ACM Trans. Algorithms (IF 1.3) Pub Date : 2023-03-09 Carla Groenland, Gwenaël Joret, Wojciech Nadara, Bartosz Walczak
We describe a polynomial-time algorithm which, given a graph G with treewidth t, approximates the pathwidth of G to within a ratio of \(O(t\sqrt {\log t})\). This is the first algorithm to achieve an f(t)-approximation for some function f. Our approach builds on the following key insight: every graph with large pathwidth has large treewidth or contains a subdivision of a large complete binary tree
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A PTAS for Capacitated Vehicle Routing on Trees ACM Trans. Algorithms (IF 1.3) Pub Date : 2023-03-10 Claire Mathieu, Hang Zhou
We give a polynomial time approximation scheme (PTAS) for the unit demand capacitated vehicle routing problem (CVRP) on trees, for the entire range of the tour capacity. The result extends to the splittable CVRP.
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Robust Algorithms for TSP and Steiner Tree ACM Trans. Algorithms (IF 1.3) Pub Date : 2023-03-09 Arun Ganesh, Bruce M. Maggs, Debmalya Panigrahi
Robust optimization is a widely studied area in operations research, where the algorithm takes as input a range of values and outputs a single solution that performs well for the entire range. Specifically, a robust algorithm aims to minimize regret, defined as the maximum difference between the solution’s cost and that of an optimal solution in hindsight once the input has been realized. For graph
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Universal Algorithms for Clustering Problems ACM Trans. Algorithms (IF 1.3) Pub Date : 2023-03-09 Arun Ganesh, Bruce M. Maggs, Debmalya Panigrahi
This article presents universal algorithms for clustering problems, including the widely studied k-median, k-means, and k-center objectives. The input is a metric space containing all potential client locations. The algorithm must select k cluster centers such that they are a good solution for any subset of clients that actually realize. Specifically, we aim for low regret, defined as the maximum over
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Approximation Schemes for Capacitated Vehicle Routing on Graphs of Bounded Treewidth, Bounded Doubling, or Highway Dimension ACM Trans. Algorithms (IF 1.3) Pub Date : 2023-03-09 Aditya Jayaprakash, Mohammad R. Salavatipour
In this article, we present Approximation Schemes for Capacitated Vehicle Routing Problem (CVRP) on several classes of graphs. In CVRP, introduced by Dantzig and Ramser in 1959 [14], we are given a graph G=(V,E) with metric edges costs, a depot r ∈ V, and a vehicle of bounded capacity Q. The goal is to find a minimum cost collection of tours for the vehicle that returns to the depot, each visiting
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Approximating (k,ℓ)-Median Clustering for Polygonal Curves ACM Trans. Algorithms (IF 1.3) Pub Date : 2023-02-23 Maike Buchin, Anne Driemel, Dennis Rohde
In 2015, Driemel, Krivošija, and Sohler introduced the k,ℓ-median clustering problem for polygonal curves under the Fréchet distance. Given a set of input curves, the problem asks to find k median curves of at most ℓ vertices each that minimize the sum of Fréchet distances over all input curves to their closest median curve. A major shortcoming of their algorithm is that the input curves are restricted
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Online Metric Algorithms with Untrusted Predictions ACM Trans. Algorithms (IF 1.3) Pub Date : 2023-02-22 Antonios Antoniadis, Christian Coester, Marek Eliáš, Adam Polak, Bertrand Simon
Machine-learned predictors, although achieving very good results for inputs resembling training data, cannot possibly provide perfect predictions in all situations. Still, decision-making systems that are based on such predictors need not only benefit from good predictions, but should also achieve a decent performance when the predictions are inadequate. In this paper, we propose a prediction setup
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Counting Homomorphic Cycles in Degenerate Graphs ACM Trans. Algorithms (IF 1.3) Pub Date : 2023-02-20 Lior Gishboliner, Yevgeny Levanzov, Asaf Shapira, Raphael Yuster
Since counting subgraphs in general graphs is, by and large, a computationally demanding problem, it is natural to try and design fast algorithms for restricted families of graphs. One such family that has been extensively studied is that of graphs of bounded degeneracy (e.g., planar graphs). This line of work, which started in the early 80’s, culminated in a recent work of Gishboliner et al., which
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Monotone Edge Flips to an Orientation of Maximum Edge-Connectivity à la Nash-Williams ACM Trans. Algorithms (IF 1.3) Pub Date : 2023-02-20 Takehiro Ito, Yuni Iwamasa, Naonori Kakimura, Naoyuki Kamiyama, Yusuke Kobayashi, Shun-Ichi Maezawa, Yuta Nozaki, Yoshio Okamoto, Kenta Ozeki
We initiate the study of k-edge-connected orientations of undirected graphs through edge flips for k ≥ 2. We prove that in every orientation of an undirected 2k-edge-connected graph, there exists a sequence of edges such that flipping their directions one by one does not decrease the edge connectivity, and the final orientation is k-edge connected. This yields an “edge-flip based” new proof of Nash-Williams’
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Competitive Algorithms for Generalized k-Server in Uniform Metrics ACM Trans. Algorithms (IF 1.3) Pub Date : 2023-02-20 Nikhil Bansal, Marek Eliáš, Grigorios Koumoutsos, Jesper Nederlof
The generalized k-server problem is a far-reaching extension of the k-server problem with several applications. Here, each server si lies in its own metric space Mi. A request is a k-tuple r = (r1,r2,… ,rk, which is served by moving some server si to the point ri ∈ Mi, and the goal is to minimize the total distance traveled by the servers. Despite much work, no f(k)-competitive algorithm is known for
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A Linear-Time n0.4-Approximation for Longest Common Subsequence ACM Trans. Algorithms (IF 1.3) Pub Date : 2023-02-20 Karl Bringmann, Vincent Cohen-Addad, Debarati Das
We consider the classic problem of computing the Longest Common Subsequence (LCS) of two strings of length n. The 40-year-old quadratic-time dynamic programming algorithm has recently been shown to be near-optimal by Abboud, Backurs, and Vassilevska Williams [FOCS’15] and Bringmann and Künnemann [FOCS’15] assuming the Strong Exponential Time Hypothesis. This has led the community to look for subquadratic