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Sublinear Time Approximation of the Cost of a Metric [math]-Nearest Neighbor Graph SIAM J. Comput. (IF 1.6) Pub Date : 2024-04-17 Artur Czumaj, Christian Sohler
SIAM Journal on Computing, Volume 53, Issue 2, Page 524-571, April 2024. Abstract. Let [math] be an [math]-point metric space. We assume that [math] is given in the distance oracle model, that is, [math] and for every pair of points [math] from [math] we can query their distance [math] in constant time. A [math]-nearest neighbor ([math]-NN) graph for [math] is a directed graph [math] that has an edge
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Online List Labeling: Breaking the [math] Barrier SIAM J. Comput. (IF 1.6) Pub Date : 2024-04-11 Michael A. Bender, Alex Conway, Martín Farach-Colton, Hanna Komlós, William Kuszmaul, Nicole Wein
SIAM Journal on Computing, Ahead of Print. Abstract. The online list-labeling problem is an algorithmic primitive with a large literature of upper bounds, lower bounds, and applications. The goal is to store a dynamically changing set of [math] items in an array of [math] slots, while maintaining the invariant that the items appear in sorted order and while minimizing the relabeling cost, defined to
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Almost Optimal SuperConstant-Pass Streaming Lower Bounds for Reachability SIAM J. Comput. (IF 1.6) Pub Date : 2024-04-09 Lijie Chen, Gillat Kol, Dmitry Paramonov, Raghuvansh R. Saxena, Zhao Song, Huacheng Yu
SIAM Journal on Computing, Ahead of Print. Abstract. We give an almost quadratic [math] lower bound on the space usage of any [math]-pass streaming algorithm solving the (directed) [math]-[math] reachability problem. This means that any such algorithm must essentially store the entire graph. As corollaries, we obtain almost quadratic space lower bounds for additional fundamental problems, including
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Rigid Matrices from Rectangular PCPs SIAM J. Comput. (IF 1.6) Pub Date : 2024-04-03 Amey Bhangale, Prahladh Harsha, Orr Paradise, Avishay Tal
SIAM Journal on Computing, Volume 53, Issue 2, Page 480-523, April 2024. Abstract. We introduce a variant of Probabilistically Checkable Proofs (PCPs) that we refer to as rectangular PCPs, wherein proofs are thought of as square matrices, and the random coins used by the verifier can be partitioned into two disjoint sets, one determining the row of each query and the other determining the column. We
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Rounds vs. Communication Tradeoffs for Maximal Independent Sets SIAM J. Comput. (IF 1.6) Pub Date : 2024-03-25 Sepehr Assadi, Gillat Kol, Zhijun Zhang
SIAM Journal on Computing, Ahead of Print. Abstract. We consider the problem of finding a maximal independent set (MIS) in the shared blackboard communication model with vertex-partitioned inputs. There are [math] players corresponding to vertices of an undirected graph, and each player sees the edges incident on its vertex; this way, each edge is known by both its endpoints and is thus shared by two
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Parameterized Complexity of Untangling Knots SIAM J. Comput. (IF 1.6) Pub Date : 2024-03-21 Clément Legrand-Duchesne, Ashutosh Rai, Martin Tancer
SIAM Journal on Computing, Volume 53, Issue 2, Page 431-479, April 2024. Abstract. Deciding whether a diagram of a knot can be untangled with a given number of moves (as a part of the input) is known to be NP-complete. In this paper we determine the parameterized complexity of this problem with respect to a natural parameter called defect. Roughly speaking, it measures the efficiency of the moves used
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Improved List-Decodability and List-Recoverability of Reed–Solomon Codes via Tree Packings SIAM J. Comput. (IF 1.6) Pub Date : 2024-03-19 Zeyu Guo, Ray Li, Chong Shangguan, Itzhak Tamo, Mary Wootters
SIAM Journal on Computing, Volume 53, Issue 2, Page 389-430, April 2024. Abstract. This paper shows that there exist Reed–Solomon (RS) codes, over exponentially large finite fields in the code length, that are combinatorially list-decodable well beyond the Johnson radius, in fact almost achieving the list-decoding capacity. In particular, we show that for any [math] there exist RS codes with rate [math]
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Sharp Thresholds in Random Simple Temporal Graphs SIAM J. Comput. (IF 1.6) Pub Date : 2024-03-19 Arnaud Casteigts, Michael Raskin, Malte Renken, Viktor Zamaraev
SIAM Journal on Computing, Volume 53, Issue 2, Page 346-388, April 2024. Abstract. A graph whose edges only appear at certain points in time is called a temporal graph (among other names). Such a graph is temporally connected if each ordered pair of vertices is connected by a path which traverses edges in chronological order (i.e., a temporal path). In this paper, we consider a simple model of random
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Fast Metric Embedding into the Hamming Cube SIAM J. Comput. (IF 1.6) Pub Date : 2024-03-14 Sjoerd Dirksen, Shahar Mendelson, Alexander Stollenwerk
SIAM Journal on Computing, Volume 53, Issue 2, Page 315-345, April 2024. Abstract. We consider the problem of embedding a subset of [math] into a low-dimensional Hamming cube in an almost isometric way. We construct a simple, data-oblivious, and computationally efficient map that achieves this task with high probability; we first apply a specific structured random matrix, which we call the double circulant
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Fixed-Parameter Algorithms for the Kneser and Schrijver Problems SIAM J. Comput. (IF 1.6) Pub Date : 2024-03-13 Ishay Haviv
SIAM Journal on Computing, Volume 53, Issue 2, Page 287-314, April 2024. Abstract. The Kneser graph [math] is defined for integers [math] and [math] with [math] as the graph whose vertices are all the [math]-subsets of [math] where two such sets are adjacent if they are disjoint. The Schrijver graph [math] is defined as the subgraph of [math] induced by the collection of all [math]-subsets of [math]
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Decentralized Low-Stretch Trees via Low Diameter Graph Decompositions SIAM J. Comput. (IF 1.6) Pub Date : 2024-03-13 Ruben Becker, Yuval Emek, Mohsen Ghaffari, Christoph Lenzen
SIAM Journal on Computing, Volume 53, Issue 2, Page 247-286, April 2024. Abstract. We study the problem of approximating the distances in an undirected weighted graph [math] by the distances in trees based on the notion of stretch. Focusing on decentralized models of computation such as the [math], [math], and semi-streaming models, our main results are as follows: (1) We develop a simple randomized
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Reachability Preservers: New Extremal Bounds and Approximation Algorithms SIAM J. Comput. (IF 1.6) Pub Date : 2024-03-13 Amir Abboud, Greg Bodwin
SIAM Journal on Computing, Volume 53, Issue 2, Page 221-246, April 2024. Abstract. We define and study reachability preservers, a graph-theoretic primitive that has been implicit in prior work on network design. Given a directed graph [math] and a set of demand pairs [math], a reachability preserver is a sparse subgraph [math] that preserves reachability between all demand pairs Our first contribution
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Counting Small Induced Subgraphs with Hereditary Properties SIAM J. Comput. (IF 1.6) Pub Date : 2024-03-12 Jacob Focke, Marc Roth
SIAM Journal on Computing, Volume 53, Issue 2, Page 189-220, April 2024. Abstract. We study the computational complexity of the problem [math] of counting [math]-vertex induced subgraphs of a graph [math] that satisfy a graph property [math]. Our main result establishes an exhaustive and explicit classification for all hereditary properties, including tight conditional lower bounds under the Exponential
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Four-Coloring [math]-Free Graphs. II. Finding an Excellent Precoloring SIAM J. Comput. (IF 1.6) Pub Date : 2024-02-28 Maria Chudnovsky, Sophie Spirkl, Mingxian Zhong
SIAM Journal on Computing, Volume 53, Issue 1, Page 146-187, February 2024. Abstract. This is the second paper in a series of two. The goal of the series is to give a polynomial-time algorithm for the 4-coloring problem and the 4-precoloring extension problem restricted to the class of graphs with no induced six-vertex path, thus proving a conjecture of Huang. Combined with previously known results
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Testing Thresholds for High-Dimensional Sparse Random Geometric Graphs SIAM J. Comput. (IF 1.6) Pub Date : 2024-02-27 Siqi Liu, Sidhanth Mohanty, Tselil Schramm, Elizabeth Yang
SIAM Journal on Computing, Ahead of Print. Abstract. The random geometric graph model [math] is a distribution over graphs in which the edges capture a latent geometry. To sample [math], we identify each of our [math] vertices with an independently and uniformly sampled vector from the [math]-dimensional unit sphere [math], and we connect pairs of vertices whose vectors are “sufficiently close,” such
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On Matrix Multiplication and Polynomial Identity Testing SIAM J. Comput. (IF 1.6) Pub Date : 2024-02-27 Robert Andrews
SIAM Journal on Computing, Ahead of Print. Abstract. We show that lower bounds on the border rank of matrix multiplication can be used to nontrivially derandomize polynomial identity testing for small algebraic circuits. Letting [math] denote the border rank of [math] matrix multiplication, we construct a hitting set generator with seed length [math] that hits [math]-variate circuits of multiplicative
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Four-Coloring [math]-Free Graphs. I. Extending an Excellent Precoloring SIAM J. Comput. (IF 1.6) Pub Date : 2024-02-27 Maria Chudnovsky, Sophie Spirkl, Mingxian Zhong
SIAM Journal on Computing, Volume 53, Issue 1, Page 111-145, February 2024. Abstract. This is the first paper in a series whose goal is to give a polynomial-time algorithm for the 4-coloring problem and the 4-precoloring extension problem restricted to the class of graphs with no induced six-vertex path, thus proving a conjecture of Huang. Combined with previously known results, this completes the
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Flow Time Scheduling and Prefix Beck–Fiala SIAM J. Comput. (IF 1.6) Pub Date : 2024-02-26 Nikhil Bansal, Lars Rohwedder, Ola Svensson
SIAM Journal on Computing, Ahead of Print. Abstract. We relate discrepancy theory with the classic scheduling problems of minimizing max flow time and total flow time on unrelated machines. Specifically, we give a general reduction that allows us to transfer discrepancy bounds in the prefix Beck–Fiala (bounded [math]-norm) setting to bounds on the flow time of an optimal schedule. Combining our reduction
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Online Edge Coloring via Tree Recurrences and Correlation Decay SIAM J. Comput. (IF 1.6) Pub Date : 2024-02-26 Janardhan Kulkarni, Yang P. Liu, Ashwin Sah, Mehtaab S. Sawhney, Jakub Tarnawski
SIAM Journal on Computing, Volume 53, Issue 1, Page 87-110, February 2024. Abstract. We give an online algorithm that with high probability computes a [math] edge coloring on a graph [math] with maximum degree [math] under online edge arrivals against oblivious adversaries, making first progress on the conjecture of Bar-Noy, Motwani, and Naor in this general setting. Our algorithm is based on reducing
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Nondeterministic Quasi-Polynomial Time is Average-Case Hard for [math] Circuits SIAM J. Comput. (IF 1.6) Pub Date : 2024-02-23 Lijie Chen
SIAM Journal on Computing, Ahead of Print. Abstract. Following the seminal work of [R. R. Williams, J. ACM, 61 (2014)], in a recent breakthrough, [C. D. Murray and R. R. Williams, STOC 2018] proved that [math] (nondeterministic quasi-polynomial time) does not have polynomial-size [math] circuits (constant depth circuits consisting of [math]/[math]/[math] gates for a fixed constant [math], a frontier
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Clustering Mixtures with Almost Optimal Separation in Polynomial Time SIAM J. Comput. (IF 1.6) Pub Date : 2024-02-22 Jerry Li, Allen Liu
SIAM Journal on Computing, Ahead of Print. Abstract. We consider the problem of clustering mixtures of mean-separated Gaussians in high dimensions. We are given samples from a mixture of [math] identity covariance Gaussians, so that the minimum pairwise distance between any two pairs of means is at least [math], for some parameter [math], and the goal is to recover the ground truth clustering of these
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Quasi-Polynomial Time Approximation Schemes for the Maximum Weight Independent Set Problem in [math]-Free Graphs SIAM J. Comput. (IF 1.6) Pub Date : 2024-02-21 Maria Chudnovsky, Marcin Pilipczuk, Michał Pilipczuk, Stéphan Thomassé
SIAM Journal on Computing, Volume 53, Issue 1, Page 47-86, February 2024. Abstract. In the Maximum Independent Set problem we are asked to find a set of pairwise nonadjacent vertices in a given graph with the maximum possible cardinality. In general graphs, this classical problem is known to be NP-hard and hard to approximate within a factor of [math] for any [math]. Due to this, investigating the
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The Shortest Even Cycle Problem Is Tractable SIAM J. Comput. (IF 1.6) Pub Date : 2024-02-15 Andreas Björklund, Thore Husfeldt, Petteri Kaski
SIAM Journal on Computing, Ahead of Print. Abstract. Given a directed graph as input, we show how to efficiently find a shortest (directed, simple) cycle on an even number of vertices. As far as we know, no polynomial-time algorithm was previously known for this problem. In fact, finding any even cycle in a directed graph in polynomial time was open for more than two decades until Robertson, Seymour
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Hardness of Random Optimization Problems for Boolean Circuits, Low-Degree Polynomials, and Langevin Dynamics SIAM J. Comput. (IF 1.6) Pub Date : 2024-02-13 David Gamarnik, Aukosh Jagannath, Alexander S. Wein
SIAM Journal on Computing, Volume 53, Issue 1, Page 1-46, February 2024. Abstract. We consider the problem of finding nearly optimal solutions of optimization problems with random objective functions. Such problems arise widely in the theory of random graphs, theoretical computer science, and statistical physics. Two concrete problems we consider are (a) optimizing the Hamiltonian of a spherical or
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A Strong Version of Cobham’s Theorem SIAM J. Comput. (IF 1.6) Pub Date : 2024-01-17 Philipp Hieronymi, Chris Schulz
SIAM Journal on Computing, Ahead of Print. Abstract. Let [math] be two multiplicatively independent integers. Cobham’s famous theorem states that a set [math] is both [math]-recognizable and [math]-recognizable if and only if it is definable in Presburger arithmetic. Here we show the following strengthening: let [math] be [math]-recognizable, and let [math] be [math]-recognizable such that both [math]
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Discrepancy Minimization via a Self-Balancing Walk SIAM J. Comput. (IF 1.6) Pub Date : 2024-01-12 Ryan Alweiss, Yang P. Liu, Mehtaab S. Sawhney
SIAM Journal on Computing, Ahead of Print. Abstract. We study discrepancy minimization for vectors in [math] under various settings. The main result is the analysis of a new simple random process in high dimensions through a comparison argument. As corollaries, we obtain bounds which are tight up to logarithmic factors for online vector balancing against oblivious adversaries, resolving several questions
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Non-Black-Box Worst-Case to Average-Case Reductions Within [math] SIAM J. Comput. (IF 1.6) Pub Date : 2023-12-15 Shuichi Hirahara
SIAM Journal on Computing, Volume 52, Issue 6, Page FOCS18-349-FOCS18-382, December 2023. Abstract. There are significant obstacles to establishing an equivalence between the worst-case and average-case hardness of [math]. Several results suggest that black-box worst-case to average-case reductions are not likely to be used for reducing any worst-case problem outside [math] to a distributional [math]
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Special Section on the Fifty-Ninth Annual IEEE Symposium on Foundations of Computer Science (2018) SIAM J. Comput. (IF 1.6) Pub Date : 2023-12-14 Elette Boyle, Vincent Cohen-Addad, Alexandra Kolla, Mikkel Thorup
SIAM Journal on Computing, Volume 52, Issue 6, Page FOCS18-i-FOCS18-i, December 2023.
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A Structural Theorem for Local Algorithms with Applications to Coding, Testing, and Verification SIAM J. Comput. (IF 1.6) Pub Date : 2023-12-06 Marcel Dall’Agnol, Tom Gur, Oded Lachish
SIAM Journal on Computing, Volume 52, Issue 6, Page 1413-1463, December 2023. Abstract. We prove a general structural theorem for a wide family of local algorithms, which includes property testers, local decoders, and probabilistically checkable proofs of proximity. Namely, we show that the structure of every algorithm that makes [math] adaptive queries and satisfies a natural robustness condition
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A Faster Exponential Time Algorithm for Bin Packing With a Constant Number of Bins via Additive Combinatorics SIAM J. Comput. (IF 1.6) Pub Date : 2023-11-29 Jesper Nederlof, Jakub Pawlewicz, Céline M. F. Swennenhuis, Karol Węgrzycki
SIAM Journal on Computing, Volume 52, Issue 6, Page 1369-1412, December 2023. Abstract. In the Bin Packing problem one is given [math] items with weights [math] and [math] bins with capacities [math]. The goal is to partition the items into sets [math] such that [math] for every bin [math], where [math] denotes [math]. Björklund, Husfeldt, and Koivisto [SIAM J. Comput., 39 (2009), pp. 546–563] presented
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Approximation Algorithms for LCS and LIS with Truly Improved Running Times SIAM J. Comput. (IF 1.6) Pub Date : 2023-11-17 Aviad Rubinstein, Saeed Seddighin, Zhao Song, Xiaorui Sun
SIAM Journal on Computing, Ahead of Print. Abstract. Longest common subsequence (LCS) is a classic and central problem in combinatorial optimization. While LCS admits a quadratic time solution, recent evidence suggests that solving the problem may be impossible in truly subquadratic time. A special case of LCS wherein each character appears at most once in every string is equivalent to the longest
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Breaking the Cubic Barrier for (Unweighted) Tree Edit Distance SIAM J. Comput. (IF 1.6) Pub Date : 2023-11-16 Xiao Mao
SIAM Journal on Computing, Ahead of Print. Abstract. The (unweighted) tree edit distance problem for [math] node trees asks to compute a measure of dissimilarity between two rooted trees with node labels. The current best algorithm from more than a decade ago runs in [math] time [Demaine et al., Automata, Languages and Programming, Springer, Berlin, 2007, pp. 146–157]. The same paper also showed that
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A Single-Exponential Time 2-Approximation Algorithm for Treewidth SIAM J. Comput. (IF 1.6) Pub Date : 2023-11-14 Tuukka Korhonen
SIAM Journal on Computing, Ahead of Print. Abstract. We give an algorithm that, given an [math]-vertex graph [math] and an integer [math], in time [math] either outputs a tree decomposition of [math] of width at most [math] or determines that the treewidth of [math] is larger than [math]. This is the first 2-approximation algorithm for treewidth that is faster than the known exact algorithms, and in
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Sampling Graphs without Forbidden Subgraphs and Unbalanced Expanders with Negligible Error SIAM J. Comput. (IF 1.6) Pub Date : 2023-11-14 Benny Applebaum, Eliran Kachlon
SIAM Journal on Computing, Volume 52, Issue 6, Page 1321-1368, December 2023. Abstract. Suppose that you wish to sample a random graph [math] over [math] vertices and [math] edges conditioned on the event that [math] does not contain a “small” [math]-size graph [math] (e.g., clique) as a subgraph. Assuming that most such graphs are [math]-free, the problem can be solved by a simple rejected-sampling
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Adversarial Laws of Large Numbers and Optimal Regret in Online Classification SIAM J. Comput. (IF 1.6) Pub Date : 2023-11-03 Noga Alon, Omri Ben-Eliezer, Yuval Dagan, Shay Moran, Moni Naor, Eylon Yogev
SIAM Journal on Computing, Ahead of Print. Abstract. Laws of large numbers guarantee that given a large enough sample from some population, the measure of any fixed subpopulation is well-estimated by its frequency in the sample. We study laws of large numbers in sampling processes that can affect the environment they are acting upon and interact with it. Specifically, we consider the sequential sampling
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Corrigendum: Metric Embedding via Shortest Path Decompositions SIAM J. Comput. (IF 1.6) Pub Date : 2023-10-27 Ittai Abraham, Arnold Filtser, Anupam Gupta, Ofer Neiman
SIAM Journal on Computing, Volume 52, Issue 5, Page 1319-1320, October 2023. Abstract. This note points out an error in the proof of Theorem 4 in the article “Metric Embedding via Shortest Path Decompositions,” SIAM J. Comput., 51 (2022), pp. 290–314, by the authors, and withdraws the associated claim of Theorem 4.
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Deterministic Massively Parallel Connectivity SIAM J. Comput. (IF 1.6) Pub Date : 2023-10-27 Sam Coy, Artur Czumaj
SIAM Journal on Computing, Volume 52, Issue 5, Page 1269-1318, October 2023. Abstract. We consider the problem of designing fundamental graph algorithms on the model of massively parallel computation (MPC). The input to the problem is an undirected graph [math] with [math] vertices and [math] edges and with [math] being the maximum diameter of any connected component in [math]. We consider the MPC
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Unambiguous DNFs and Alon–Saks–Seymour SIAM J. Comput. (IF 1.6) Pub Date : 2023-10-20 Kaspars Balodis, Shalev Ben-David, Mika Göös, Siddhartha Jain, Robin Kothari
SIAM Journal on Computing, Ahead of Print. Abstract. We exhibit an unambiguous [math]-DNF (disjunctive normal form) formula that requires conjunctive normal form width [math], which is optimal up to logarithmic factors. As a consequence, we get a near-optimal solution to the Alon–Saks–Seymour problem in graph theory (posed in 1991), which asks, How large a gap can there be between the chromatic number
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Optimal Mixing of Glauber Dynamics: Entropy Factorization via High-Dimensional Expansion SIAM J. Comput. (IF 1.6) Pub Date : 2023-10-20 Zongchen Chen, Kuikui Liu, Eric Vigoda
SIAM Journal on Computing, Ahead of Print. Abstract. We prove an optimal mixing time bound for the single-site update Markov chain known as the Glauber dynamics or Gibbs sampling in a variety of settings. Our work presents an improved version of the spectral independence approach of Anari, Liu, and Oveis Gharan [Proceedings of the 61st Annual IEEE Symposium on Foundations of Computer Science (FOCS)
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Finding Maximum Edge-Disjoint Paths Between Multiple Terminals SIAM J. Comput. (IF 1.6) Pub Date : 2023-10-17 Satoru Iwata, Yu Yokoi
SIAM Journal on Computing, Volume 52, Issue 5, Page 1230-1268, October 2023. Abstract. Let [math] be a multigraph with a set [math] of terminals. A path in [math] is called a [math]-path if its ends are distinct vertices in [math] and no internal vertices belong to [math]. In 1978, Mader showed a characterization of the maximum number of edge-disjoint [math]-paths. In this paper, we provide a combinatorial
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Definable Ellipsoid Method, Sums-of-Squares Proofs, and the Graph Isomorphism Problem SIAM J. Comput. (IF 1.6) Pub Date : 2023-10-16 Albert Atserias, Joanna Fijalkow
SIAM Journal on Computing, Volume 52, Issue 5, Page 1193-1229, October 2023. Abstract. The ellipsoid method is an algorithm that solves the (weak) feasibility and linear optimization problems for convex sets by making oracle calls to their (weak) separation problem. We observe that the previously known method for showing that this reduction can be done in fixed-point logic with counting (FPC) for linear
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Deterministic Near-Optimal Approximation Algorithms for Dynamic Set Cover SIAM J. Comput. (IF 1.6) Pub Date : 2023-10-06 Sayan Bhattacharya, Monika Henzinger, Danupon Nanongkai, Xiaowei Wu
SIAM Journal on Computing, Volume 52, Issue 5, Page 1132-1192, October 2023. Abstract. In the dynamic minimum set cover problem, the challenge is to minimize the update time while guaranteeing a close-to-optimal [math] approximation factor. (Throughout, [math], [math], [math], and [math] are parameters denoting the maximum number of elements, the number of sets, the frequency, and the cost range.)
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Exact-Size Sampling of Enriched Trees in Linear Time SIAM J. Comput. (IF 1.6) Pub Date : 2023-10-04 Konstantinos Panagiotou, Leon Ramzews, Benedikt Stufler
SIAM Journal on Computing, Volume 52, Issue 5, Page 1097-1131, October 2023. Abstract. We create a novel connection between Boltzmann sampling methods and Devroye’s algorithm to develop highly efficient sampling procedures that generate objects from important combinatorial classes with a given size [math] in expected time [math]. This performance is best possible and significantly improves the state
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A Polynomial-Time Algorithm for 1/2-Well-Supported Nash Equilibria in Bimatrix Games SIAM J. Comput. (IF 1.6) Pub Date : 2023-09-12 Argyrios Deligkas, Michail Fasoulakis, Evangelos Markakis
SIAM Journal on Computing, Volume 52, Issue 5, Page 1083-1096, October 2023. Abstract. Since the seminal PPAD-completeness result for computing a Nash equilibrium even in two-player games, an important line of research has focused on relaxations achievable in polynomial time. In this paper, we consider the notion of an [math]-well-supported Nash equilibrium, where [math] corresponds to the approximation
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Average Sensitivity of Graph Algorithms SIAM J. Comput. (IF 1.6) Pub Date : 2023-08-14 Nithin Varma, Yuichi Yoshida
SIAM Journal on Computing, Volume 52, Issue 4, Page 1039-1081, August 2023. Abstract. Modern applications of graph algorithms often involve the use of the output sets (usually, a subset of edges or vertices of the input graph) as inputs to other algorithms. Since the input graphs of interest are large and dynamic, it is desirable for an algorithm’s output to not change drastically when a few random
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Dequantizing the Quantum Singular Value Transformation: Hardness and Applications to Quantum Chemistry and the Quantum PCP Conjecture SIAM J. Comput. (IF 1.6) Pub Date : 2023-08-10 Sevag Gharibian, François Le Gall
SIAM Journal on Computing, Volume 52, Issue 4, Page 1009-1038, August 2023. Abstract. The Quantum Singular Value Transformation (QSVT) is a recent technique that gives a unified framework to describe most quantum algorithms discovered so far, and may lead to the development of novel quantum algorithms. In this paper we investigate the hardness of classically simulating the QSVT. A recent result by
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Sublinear Algorithms for Local Graph-Centrality Estimation SIAM J. Comput. (IF 1.6) Pub Date : 2023-08-10 Marco Bressan, Enoch Peserico, Luca Pretto
SIAM Journal on Computing, Volume 52, Issue 4, Page 968-1008, August 2023. Abstract. We study the complexity of local graph-centrality estimation, with the goal of approximating the centrality score of a given target node while exploring only a sublinear number of nodes/arcs of the graph and performing a sublinear number of elementary operations. We develop a technique, which we apply to PageRank and
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Deterministic [math]-Approximation for Submodular Maximization over a Matroid SIAM J. Comput. (IF 1.6) Pub Date : 2023-07-27 Niv Buchbinder, Moran Feldman, Mohit Garg
SIAM Journal on Computing, Volume 52, Issue 4, Page 945-967, August 2023. Abstract. We study the problem of maximizing a monotone submodular function subject to a matroid constraint and present a deterministic algorithm that achieves [math]-approximation for the problem (for some [math]). This algorithm is the first deterministic algorithm known to improve over the [math]-approximation ratio of the
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Why Extension-Based Proofs Fail SIAM J. Comput. (IF 1.6) Pub Date : 2023-07-25 Dan Alistarh, James Aspnes, Faith Ellen, Rati Gelashvili, Leqi Zhu
SIAM Journal on Computing, Volume 52, Issue 4, Page 913-944, August 2023. Abstract. We introduce extension-based proofs, a class of impossibility proofs that includes valency arguments. They are modelled as an interaction between a prover and a protocol. Using proofs based on combinatorial topology, it has been shown that it is impossible to deterministically solve [math]-set agreement among [math]
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Hitting Minors on Bounded Treewidth Graphs. IV. An Optimal Algorithm SIAM J. Comput. (IF 1.6) Pub Date : 2023-07-20 Julien Baste, Ignasi Sau, Dimitrios M. Thilikos
SIAM Journal on Computing, Volume 52, Issue 4, Page 865-912, August 2023. Abstract. For a fixed finite collection of graphs [math] the [math]-M-Deletion problem is as follows: given an [math]-vertex input graph [math] find the minimum number of vertices that intersect all minor models in [math] of the graphs in [math]. by Courcelle’s Theorem, this problem can be solved in time [math] where [math] is
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The Approximation Ratio of the k-Opt Heuristic for the Euclidean Traveling Salesman Problem SIAM J. Comput. (IF 1.6) Pub Date : 2023-07-20 Ulrich A. Brodowsky, Stefan Hougardy, Xianghui Zhong
SIAM Journal on Computing, Volume 52, Issue 4, Page 841-864, August 2023. Abstract. The [math]-Opt heuristic is a simple improvement heuristic for the traveling salesman problem. It starts with an arbitrary tour and then repeatedly replaces [math] edges of the tour by [math] other edges, as long as this yields a shorter tour. We will prove that for the 2-dimensional Euclidean traveling salesman problem
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Improved List Decoding of Folded Reed-Solomon and Multiplicity Codes SIAM J. Comput. (IF 1.6) Pub Date : 2023-06-15 Swastik Kopparty, Noga Ron-Zewi, Shubhangi Saraf, Mary Wootters
SIAM Journal on Computing, Volume 52, Issue 3, Page 794-840, June 2023. Abstract. We show new and improved list decoding properties of folded Reed–Solomon (RS) codes and multiplicity codes. Both of these families of codes are based on polynomials over finite fields, and both have been the source of recent advances in coding theory: folded RS codes were the first known explicit construction of capacity-achieving
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Near-Optimal Learning of Tree-Structured Distributions by Chow and Liu SIAM J. Comput. (IF 1.6) Pub Date : 2023-06-15 Arnab Bhattacharyya, Sutanu Gayen, Eric Price, Vincent Y. F. Tan, N. V. Vinodchandran
SIAM Journal on Computing, Volume 52, Issue 3, Page 761-793, June 2023. Abstract. We provide finite sample guarantees for the classical Chow–Liu algorithm [Chow and Liu, IEEE Trans. Inform. Theory, 14 (1968), pp. 462–467] to learn a tree-structured graphical model of a distribution. For a distribution [math] on [math] and a tree [math] on [math] nodes, we say [math] is an [math]-approximate tree for
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An ETH-Tight Exact Algorithm for Euclidean TSP SIAM J. Comput. (IF 1.6) Pub Date : 2023-06-05 Mark de Berg, Hans L. Bodlaender, Sándor Kisfaludi-Bak, Sudeshna Kolay
SIAM Journal on Computing, Volume 52, Issue 3, Page 740-760, June 2023. Abstract. We study exact algorithms for Metric TSP in [math]. In the early 1990s, algorithms with [math] running time were presented for the planar case, and some years later an algorithm with [math] running time was presented for any [math]. Despite significant interest in subexponential exact algorithms over the past decade,
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Breaching the 2-Approximation Barrier for Connectivity Augmentation: A Reduction to Steiner Tree SIAM J. Comput. (IF 1.6) Pub Date : 2023-05-23 Jarosław Byrka, Fabrizio Grandoni, Afrouz Jabal Ameli
SIAM Journal on Computing, Volume 52, Issue 3, Page 718-739, June 2023. Abstract. The basic goal of survivable network design is to build a cheap network that maintains the connectivity between given sets of nodes despite the failure of a few edges/nodes. The connectivity augmentation problem ([math]) is arguably one of the most basic problems in this area: given a [math](-edge)-connected graph [math]
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Generalized Singleton Bound and List-Decoding Reed–Solomon Codes Beyond the Johnson Radius SIAM J. Comput. (IF 1.6) Pub Date : 2023-05-23 Chong Shangguan, Itzhak Tamo
SIAM Journal on Computing, Volume 52, Issue 3, Page 684-717, June 2023. Abstract. In this paper we take a combinatorial approach to the problem of list-decoding, which allows us to determine the precise relation (up to the exact constant) between the decoding radius, list size, and code rate. We prove a generalized Singleton bound for a given list size, and conjecture that the bound is tight for most
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Uniform Restricted Chase Termination SIAM J. Comput. (IF 1.6) Pub Date : 2023-05-23 Tomasz Gogacz, Jerzy Marcinkowski, Andreas Pieris
SIAM Journal on Computing, Volume 52, Issue 3, Page 641-683, June 2023. Abstract. The chase procedure is a fundamental algorithmic tool in database theory with a variety of applications. A central problem concerning the chase procedure is uniform (a.k.a. all-instances) chase termination: for a given set of tuple-generating dependencies (TGDs), is it the case that the chase terminates for every input
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Special Section on the Fifty-First Annual ACM Symposium on the Theory of Computing (STOC 2019) SIAM J. Comput. (IF 1.6) Pub Date : 2023-04-27 Dana Moshkovitz, Sushant Sachdeva
SIAM Journal on Computing, Volume 52, Issue 2, Page STOC19-i-STOC19-ii, April 2023.
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Fully Dynamic Electrical Flows: Sparse Maxflow Faster Than Goldberg–Rao SIAM J. Comput. (IF 1.6) Pub Date : 2023-04-26 Yu Gao, Yang Liu, Richard Peng
SIAM Journal on Computing, Ahead of Print. Abstract. We give an algorithm for computing exact maximum flows on graphs with [math] edges and integer capacities in the range [math] in [math] time. We use [math] to suppress logarithmic factors in [math]. For sparse graphs with polynomially bounded integer capacities, this is the first improvement over the [math] time bound from Goldberg and Rao [J. ACM
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An Optimal Separation of Randomized and Quantum Query Complexity SIAM J. Comput. (IF 1.6) Pub Date : 2023-04-26 Alexander A. Sherstov, Andrey A. Storozhenko, Pei Wu
SIAM Journal on Computing, Volume 52, Issue 2, Page 525-567, April 2023. Abstract. We prove that for every decision tree, the absolute values of the Fourier coefficients of a given order [math] sum to at most [math], where [math] is the number of variables, [math] is the tree depth, and [math] is an absolute constant. This bound is essentially tight and settles a conjecture due to Tal [Towards optimal