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  • Oblivious Resampling Oracles and Parallel Algorithms for the Lopsided Lovász Local Lemma
    ACM Trans. Algorithms (IF 0.758) Pub Date : 2020-12-31
    David G. Harris

    The Lovász Local Lemma (LLL) shows that, for a collection of “bad” events B in a probability space that are not too likely and not too interdependent, there is a positive probability that no events in B occur. Moser and Tardos (2010) gave sequential and parallel algorithms that transformed most applications of the variable-assignment LLL into efficient algorithms. A framework of Harvey and Vondrák

  • Deterministic APSP, Orthogonal Vectors, and More: Quickly Derandomizing Razborov-Smolensky
    ACM Trans. Algorithms (IF 0.758) Pub Date : 2020-12-31
    Timothy M. Chan; R. Ryan Williams

    We show how to solve all-pairs shortest paths on n nodes in deterministic n3>/2>Ω ( √ log n) time, and how to count the pairs of orthogonal vectors among n 0−1 vectors in d = clog n dimensions in deterministic n2−1/O(log c) time. These running times essentially match the best known randomized algorithms of Williams [46] and Abboud, Williams, and Yu [8], respectively, and the ability to count was open

  • Tight Bounds for Online TSP on the Line
    ACM Trans. Algorithms (IF 0.758) Pub Date : 2020-12-31
    Antje Bjelde; Jan Hackfeld; Yann Disser; Christoph Hansknecht; Maarten Lipmann; Julie Meißner; Miriam SchlÖter; Kevin Schewior; Leen Stougie

    We consider the online traveling salesperson problem (TSP), where requests appear online over time on the real line and need to be visited by a server initially located at the origin. We distinguish between closed and open online TSP, depending on whether the server eventually needs to return to the origin or not. While online TSP on the line is a very natural online problem that was introduced more

  • Zeros of Holant Problems: Locations and Algorithms
    ACM Trans. Algorithms (IF 0.758) Pub Date : 2020-12-31
    Heng Guo; Chao Liao; Pinyan Lu; Chihao Zhang

    We present fully polynomial-time (deterministic or randomised) approximation schemes for Holant problems, defined by a non-negative constraint function satisfying a generalised second-order recurrence modulo in a couple of exceptional cases. As a consequence, any non-negative Holant problem on cubic graphs has an efficient approximation algorithm unless the problem is equivalent to approximately counting

  • Fine-grained Complexity Analysis of Two Classic TSP Variants
    ACM Trans. Algorithms (IF 0.758) Pub Date : 2020-12-31
    Mark de Berg; Kevin Buchin; Bart M. P. Jansen; Gerhard Woeginger

    We analyze two classic variants of the TRAVELING SALESMAN PROBLEM (TSP) using the toolkit of fine-grained complexity. Our first set of results is motivated by the BITONIC TSP problem: given a set of n points in the plane, compute a shortest tour consisting of two monotone chains. It is a classic dynamic-programming exercise to solve this problem in O(n2) time. While the near-quadratic dependency of

  • Randomized Contractions Meet Lean Decompositions
    ACM Trans. Algorithms (IF 0.758) Pub Date : 2020-12-31
    Marek Cygan; Paweł Komosa; Daniel Lokshtanov; Marcin Pilipczuk; Michał Pilipczuk; Saket Saurabh; Magnus Wahlström

    We show an algorithm that, given an n-vertex graph G and a parameter k, in time 2O(k log k) nO(1) finds a tree decomposition of G with the following properties: — every adhesion of the tree decomposition is of size at most k, and — every bag of the tree decomposition is (i,i)-unbreakable in G for every 1 ⩽ i ⩽ k. Here, a set X ⊆ V(G) is (a,b)-unbreakable in G if for every separation (A,B) of order

  • Optimal Substring Equality Queries with Applications to Sparse Text Indexing
    ACM Trans. Algorithms (IF 0.758) Pub Date : 2020-12-31
    Nicola Prezza

    We consider the problem of encoding a string of length n from an integer alphabet of size σ so access, substring equality, and Longest Common Extension (LCE) queries can be answered efficiently. We describe a new space-optimal data structure supporting logarithmic-time queries. Access and substring equality query times can furthermore be improved to the optimal O(1) if O(log n) additional precomputed

  • Optimal-Time Dictionary-Compressed Indexes
    ACM Trans. Algorithms (IF 0.758) Pub Date : 2020-12-31
    Anders Roy Christiansen; Mikko Berggren Ettienne; Tomasz Kociumaka; Gonzalo Navarro; Nicola Prezza

    We describe the first self-indexes able to count and locate pattern occurrences in optimal time within a space bounded by the size of the most popular dictionary compressors. To achieve this result, we combine several recent findings, including string attractors—new combinatorial objects encompassing most known compressibility measures for highly repetitive texts—and grammars based on locally consistent

  • Journey to the Center of the Point Set
    ACM Trans. Algorithms (IF 0.758) Pub Date : 2020-12-31
    Sariel Har-Peled; Mitchell Jones

    Let P be a set of n points in R d. For a parameter α ∈ (0,1), an α-centerpoint of P is a point p ∈ R d such that all closed halfspaces containing P also contain at least α n points of P. We revisit an algorithm of Clarkson et al. [1996] that computes (roughly) a 1/(4d2)-centerpoint in Õ(d9) randomized time, where Õ hides polylogarithmic terms. We present an improved algorithm that can compute centerpoints

  • Edge Estimation with Independent Set Oracles
    ACM Trans. Algorithms (IF 0.758) Pub Date : 2020-09-16
    Paul Beame; Sariel Har-Peled; Sivaramakrishnan Natarajan Ramamoorthy; Cyrus Rashtchian; Makrand Sinha

    We study the task of estimating the number of edges in a graph, where the access to the graph is provided via an independent set oracle. Independent set queries draw motivation from group testing and have applications to the complexity of decision versus counting problems. We give two algorithms to estimate the number of edges in an n-vertex graph, using (i) polylog(n) bipartite independent set queries

  • A Complexity Theoretical Study of FuzzyK-Means
    ACM Trans. Algorithms (IF 0.758) Pub Date : 2020-09-16
    Johannes Blömer; Sascha Brauer; Kathrin Bujna

    The fuzzy K-means problem is a popular generalization of the well-known K-means problem to soft clusterings. In this article, we present the first algorithmic study of the problem going beyond heuristics. Our main result is that, assuming a constant number of clusters, there is a polynomial time approximation scheme for the fuzzy K-means problem. As a part of our analysis, we also prove the existence

  • Point-Width and Max-CSPs
    ACM Trans. Algorithms (IF 0.758) Pub Date : 2020-09-16
    Clément Carbonnel; Miguel Romero; Stanislav Živný

    The complexity of (unbounded-arity) Max-CSPs under structural restrictions is poorly understood. The two most general hypergraph properties known to ensure tractability of Max-CSPs, β-acyclicity and bounded (incidence) MIM-width, are incomparable and lead to very different algorithms. We introduce the framework of point decompositions for hypergraphs and use it to derive a new sufficient condition

  • Parameterized Hardness of Art Gallery Problems
    ACM Trans. Algorithms (IF 0.758) Pub Date : 2020-06-19
    Édouard Bonnet; Tillmann Miltzow

    Given a simple polygon P on n vertices, two points x, y in P are said to be visible to each other if the line segment between x and y is contained in P. The Point Guard Art Gallery problem asks for a minimum set S such that every point in P is visible from a point in S. The Vertex Guard Art Gallery problem asks for such a set S subset of the vertices of P. A point in the set S is referred to as a guard

  • Symmetry Exploitation for Online Machine Covering with Bounded Migration
    ACM Trans. Algorithms (IF 0.758) Pub Date : 2020-07-06
    Waldo Gálvez; José A. Soto; José Verschae

    Online models that allow recourse can be highly effective in situations where classical online models are too pessimistic. One such problem is the online machine covering problem on identical machines. In this setting, jobs arrive one by one and must be assigned to machines with the objective of maximizing the minimum machine load. When a job arrives, we are allowed to reassign some jobs as long as

  • Approximate Single-Source Fault Tolerant Shortest Path
    ACM Trans. Algorithms (IF 0.758) Pub Date : 2020-07-06
    Surender Baswana; Keerti Choudhary; Moazzam Hussain; Liam Roditty

    Let G=(V,E) be an n-vertices m-edges directed graph with edge weights in the range [1,W] for some parameter W, and sϵ V be a designated source. In this article, we address several variants of the problem of maintaining the (1+ε)-approximate shortest path from s to each vϵ V{s} in the presence of a failure of an edge or a vertex. From the graph theory perspective, we show that G has a subgraph H with

  • Dynamic Parameterized Problems and Algorithms
    ACM Trans. Algorithms (IF 0.758) Pub Date : 2020-07-06
    Josh Alman; Matthias Mnich; Virginia Vassilevska Williams

    Fixed-parameter algorithms and kernelization are two powerful methods to solve NP-hard problems. Yet so far those algorithms have been largely restricted to static inputs. In this article, we provide fixed-parameter algorithms and kernelizations for fundamental NP-hard problems with dynamic inputs. We consider a variety of parameterized graph and hitting set problems that are known to have f(k)n1+o(1)

  • The Non-Uniformk-Center Problem
    ACM Trans. Algorithms (IF 0.758) Pub Date : 2020-06-19
    Deeparnab Chakrabarty; Prachi Goyal; Ravishankar Krishnaswamy

    In this article, we introduce and study the Non-Uniform k-Center (NUkC) problem. Given a finite metric space (X, d) and a collection of balls of radii { r1 ≥ … ≥ rk}, the NUkC problem is to find a placement of their centers in the metric space and find the minimum dilation α, such that the union of balls of radius α ⋅ ri around the ith center covers all the points in X. This problem naturally arises

  • A Colored Path Problem and Its Applications
    ACM Trans. Algorithms (IF 0.758) Pub Date : 2020-06-19
    Eduard Eiben; Iyad Kanj

    Given a set of obstacles and two points in the plane, is there a path between the two points that does not cross more than k different obstacles? Equivalently, can we remove k obstacles so that there is an obstacle-free path between the two designated points? This is a fundamental NP-hard problem that has undergone a tremendous amount of research work. The problem can be formulated and generalized

  • Tree Edit Distance Cannot be Computed in Strongly Subcubic Time (Unless APSP Can)
    ACM Trans. Algorithms (IF 0.758) Pub Date : 2020-07-06
    Karl Bringmann; Paweł Gawrychowski; Shay Mozes; Oren Weimann

    The edit distance between two rooted ordered trees with n nodes labeled from an alphabet Ʃ is the minimum cost of transforming one tree into the other by a sequence of elementary operations consisting of deleting and relabeling existing nodes, as well as inserting new nodes. Tree edit distance is a well-known generalization of string edit distance. The fastest known algorithm for tree edit distance

  • Maximum Matching in the Online Batch-arrival Model
    ACM Trans. Algorithms (IF 0.758) Pub Date : 2020-07-20
    Euiwoong Lee; Sahil Singla

    Consider a two-stage matching problem, where edges of an input graph are revealed in two stages (batches) and in each stage we have to immediately and irrevocably extend our matching using the edges from that stage. The natural greedy algorithm is half competitive. Even though there is a huge literature on online matching in adversarial vertex arrival model, no positive results were previously known

  • Deterministic Sparse Suffix Sorting in the Restore Model
    ACM Trans. Algorithms (IF 0.758) Pub Date : 2020-07-12
    Johannes Fischer; Tomohiro I; Dominik Köppl

    Given a text T of length n, we propose a deterministic online algorithm computing the sparse suffix array and the sparse longest common prefix array of T in O(c √ lg n + m lg m lg n lg* n) time with O(m) words of space under the premise that the space of T is rewritable, where m ≤ n is the number of suffixes to be sorted (provided online and arbitrarily), and c is the number of characters with m ≤

  • Polylogarithmic Approximation Algorithms for Weighted-ℱ-deletion Problems
    ACM Trans. Algorithms (IF 0.758) Pub Date : 2020-07-12
    Akanksha Agrawal; Daniel Lokshtanov; Pranabendu Misra; Saket Saurabh; Meirav Zehavi

    For a family of graphs ℱ, the Weighted ℱ Vertex Deletion problem, is defined as follows: given an n-vertex undirected graph G and a weight function w: V(G)࢐ ℝ, find a minimum weight subset S⊆ V(G) such that G-S belongs to ℱ. We devise a recursive scheme to obtain O(logO(1) n)-approximation algorithms for such problems, building upon the classical technique of finding balanced separators. We obtain

  • Approximating Spanners and Directed Steiner Forest
    ACM Trans. Algorithms (IF 0.758) Pub Date : 2020-06-12
    Eden Chlamtáč; Michael Dinitz; Guy Kortsarz; Bundit Laekhanukit

    It was recently found that there are very close connections between the existence of additive spanners (subgraphs where all distances are preserved up to an additive stretch), distance preservers (subgraphs in which demand pairs have their distance preserved exactly), and pairwise spanners (subgraphs in which demand pairs have their distance preserved up to a multiplicative or additive stretch) [Abboud-Bodwin

  • Nearly ETH-tight Algorithms for Planar Steiner Tree with Terminals on Few Faces
    ACM Trans. Algorithms (IF 0.758) Pub Date : 2020-06-01
    Sándor Kisfaludi-Bak; Jesper Nederlof; Erik Jan van Leeuwen

    The STEINER TREE problem is one of the most fundamental NP-complete problems, as it models many network design problems. Recall that an instance of this problem consists of a graph with edge weights and a subset of vertices (often called terminals); the goal is to find a subtree of the graph of minimum total weight that connects all terminals. A seminal paper by Erickson et al. [Math. Oper. Res., 1987{

  • The Complexity of Cake Cutting with Unequal Shares
    ACM Trans. Algorithms (IF 0.758) Pub Date : 2020-06-01
    Ágnes Cseh; Tamás Fleiner

    An unceasing problem of our prevailing society is the fair division of goods. The problem of proportional cake cutting focuses on dividing a heterogeneous and divisible resource, the cake, among n players who value pieces according to their own measure function. The goal is to assign each player a not necessarily connected part of the cake that the player evaluates at least as much as her proportional

  • Periods of Iterations of Functions with Restricted Preimage Sizes
    ACM Trans. Algorithms (IF 0.758) Pub Date : 2020-06-01
    Rodrigo S. V. Martins; Daniel Panario; Claudio Qureshi; Eric Schmutz

    Let [n{ = {1, …, n} and let Ωn be the set of all mappings from [n{ to itself. Let f be a random uniform element of Ωn and let T(f) and B(f) denote, respectively, the least common multiple and the product of the length of the cycles of f. Harris proved in 1973 that T converges in distribution to a standard normal distribution and, in 2011, Schmutz obtained an asymptotic estimate on the logarithm of

  • Tight Bounds on Online Checkpointing Algorithms
    ACM Trans. Algorithms (IF 0.758) Pub Date : 2020-06-01
    Achiya Bar-On; Itai Dinur; Orr Dunkelman; Rani Hod; Nathan Keller; Eyal Ronen; Adi Shamir

    The problem of online checkpointing is a classical problem with numerous applications that has been studied in various forms for almost 50 years. In the simplest version of this problem, a user has to maintain k memorized checkpoints during a long computation, where the only allowed operation is to move one of the checkpoints from its old time to the current time, and his goal is to keep the checkpoints

  • Covering Small Independent Sets and Separators with Applications to Parameterized Algorithms
    ACM Trans. Algorithms (IF 0.758) Pub Date : 2020-06-01
    Daniel Lokshtanov; Fahad Panolan; Saket Saurabh; Roohani Sharma; Meirav Zehavi

    We present two new combinatorial tools for the design of parameterized algorithms. The first is a simple linear time randomized algorithm that given as input a d-degenerate graph G and an integer k, outputs an independent set Y, such that for every independent set X in G of size at most k, the probability that X is a subset of Y is at least (((d+1)kk) . k(d+1))-1. The second is a new (deterministic)

  • An Improved Isomorphism Test for Bounded-tree-width Graphs
    ACM Trans. Algorithms (IF 0.758) Pub Date : 2020-06-01
    Martin Grohe; Daniel Neuen; Pascal Schweitzer; Daniel Wiebking

    We give a new FPT algorithm testing isomorphism of n-vertex graphs of tree-width k in time 2kpolylog(k)n3, improving the FPT algorithm due to Lokshtanov, Pilipczuk, Pilipczuk, and Saurabh (FOCS 2014), which runs in time 2O(k5 log k)n5. Based on an improved version of the isomorphism-invariant graph decomposition technique introduced by Lokshtanov et al., we prove restrictions on the structure of the

  • Time- and Space-optimal Algorithm for the Many-visits TSP
    ACM Trans. Algorithms (IF 0.758) Pub Date : 2020-06-01
    André Berger; László Kozma; Matthias Mnich; Roland Vincze

    The many-visits traveling salesperson problem (MV-TSP) asks for an optimal tour of n cities that visits each city c a prescribed number kc of times. Travel costs may be asymmetric, and visiting a city twice in a row may incur a non-zero cost. The MV-TSP problem finds applications in scheduling, geometric approximation, and Hamiltonicity of certain graph families.

  • Structure Learning of H-Colorings
    ACM Trans. Algorithms (IF 0.758) Pub Date : 2020-06-01
    Antonio Blanca; Zongchen Chen; Daniel Štefankoviè; Eric Vigoda

    We study the following structure learning problem for H-colorings. For a fixed (and known) constraint graph H with q colors, given access to uniformly random H-colorings of an unknown graph G=(V,E), how many samples are required to learn the edges of G? We give a characterization of the constraint graphs H for which the problem is identifiable for every G and show that there are identifiable constraint

  • Random Walks on Small World Networks
    ACM Trans. Algorithms (IF 0.758) Pub Date : 2020-06-01
    Martin E. Dyer; Andreas Galanis; Leslie Ann Goldberg; Mark Jerrum; Eric Vigoda

    We study the mixing time of random walks on small-world networks modelled as follows: starting with the 2-dimensional periodic grid, each pair of vertices {u,v} with distance d> 1 is added as a “long-range” edge with probability proportional to d-r, where r≥ 0 is a parameter of the model. Kleinberg [33{ studied a close variant of this network model and proved that the (decentralised) routing time is

  • A PTAS for Euclidean TSP with Hyperplane Neighborhoods
    ACM Trans. Algorithms (IF 0.758) Pub Date : 2020-06-01
    Antonios Antoniadis; Krzysztof Fleszar; Ruben Hoeksma; Kevin Schewior

    In the Traveling Salesperson Problem with Neighborhoods (TSPN), we are given a collection of geometric regions in some space. The goal is to output a tour of minimum length that visits at least one point in each region. Even in the Euclidean plane, TSPN is known to be APX-hard [27{, which gives rise to studying more tractable special cases of the problem. In this article, we focus on the fundamental

  • Enumerating Minimal Dominating Sets in Kt-free Graphs and Variants
    ACM Trans. Algorithms (IF 0.758) Pub Date : 2020-06-01
    Marthe Bonamy; Oscar Defrain; Marc Heinrich; Michał Pilipczuk; Jean-Florent Raymond

    It is a long-standing open problem whether the minimal dominating sets of a graph can be enumerated in output-polynomial time. In this article we investigate this problem in graph classes defined by forbidding an induced subgraph. In particular, we provide output-polynomial time algorithms for Kt-free graphs and for several related graph classes. This answers a question of Kanté et al. about enumeration

  • Clustering in Hypergraphs to Minimize Average Edge Service Time
    ACM Trans. Algorithms (IF 0.758) Pub Date : 2020-06-01
    Ori Rottenstreich; Haim Kaplan; Avinatan Hassidim

    We study the problem of clustering the vertices of a weighted hypergraph such that on average the vertices of each edge can be covered by a small number of clusters. This problem has many applications, such as for designing medical tests, clustering files on disk servers, and placing network services on servers. The edges of the hypergraph model groups of items that are likely to be needed together

  • Improved Dynamic Graph Coloring
    ACM Trans. Algorithms (IF 0.758) Pub Date : 2020-06-01
    Shay Solomon; Nicole Wein

    This article studies the fundamental problem of graph coloring in fully dynamic graphs. Since the problem of computing an optimal coloring, or even approximating it to within n1-ε for any ε > 0, is NP-hard in static graphs, there is no hope to achieve any meaningful computational results for general graphs in the dynamic setting. It is therefore only natural to consider the combinatorial aspects of

  • Test
    ACM Trans. Algorithms (IF 0.758) Pub Date : 2020-04-30

    No abstract available.

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