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- research-articleSeptember 2024JUST ACCEPTED
- research-articleAugust 2024
Killing a Vortex
Journal of the ACM (JACM), Volume 71, Issue 4Article No.: 27, Pages 1–56https://doi.org/10.1145/3664648 - research-articleOctober 2023
Exponentially Faster Massively Parallel Maximal Matching
Journal of the ACM (JACM), Volume 70, Issue 5Article No.: 34, Pages 1–18https://doi.org/10.1145/3617360The study of approximate matching in the Massively Parallel Computations (MPC) model has recently seen a burst of breakthroughs. Despite this progress, we still have a limited understanding of maximal matching which is one of the central problems of ...
- research-articleOctober 2023
Restorable Shortest Path Tiebreaking for Edge-Faulty Graphs
Journal of the ACM (JACM), Volume 70, Issue 5Article No.: 28, Pages 1–24https://doi.org/10.1145/3603542The restoration lemma by Afek et al. [3] proves that, in an undirected unweighted graph, any replacement shortest path avoiding a failing edge can be expressed as the concatenation of two original shortest paths. However, the lemma is tiebreaking-...
- research-articleJune 2022
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- research-articleJune 2022
- research-articleJuly 2021
Almost Tight Lower Bounds for Hard Cutting Problems in Embedded Graphs
Journal of the ACM (JACM), Volume 68, Issue 4Article No.: 30, Pages 1–26https://doi.org/10.1145/3450704We prove essentially tight lower bounds, conditionally to the Exponential Time Hypothesis, for two fundamental but seemingly very different cutting problems on surface-embedded graphs: the Shortest Cut Graph problem and the Multiway Cut problem.
A cut ...
- research-articleJanuary 2020
Detecting an Odd Hole
Journal of the ACM (JACM), Volume 67, Issue 1Article No.: 5, Pages 1–12https://doi.org/10.1145/3375720We give a polynomial-time algorithm to test whether a graph contains an induced cycle with length more than three and odd.
- research-articleOctober 2019
Tight Bounds for Undirected Graph Exploration with Pebbles and Multiple Agents
Journal of the ACM (JACM), Volume 66, Issue 6Article No.: 40, Pages 1–41https://doi.org/10.1145/3356883We study the problem of deterministically exploring an undirected and initially unknown graph with n vertices either by a single agent equipped with a set of pebbles or by a set of collaborating agents. The vertices of the graph are unlabeled and cannot ...
- research-articleApril 2018
Distributed (Δ +1)-Coloring in Sublogarithmic Rounds
Journal of the ACM (JACM), Volume 65, Issue 4Article No.: 19, Pages 1–21https://doi.org/10.1145/3178120We give a new randomized distributed algorithm for (Δ +1)-coloring in the LOCAL model, running in O(√ log Δ)+ 2O(√log log n) rounds in a graph of maximum degree Δ. This implies that the (Δ +1)-coloring problem is easier than the maximal independent set ...
- research-articleMarch 2018
Spectral Properties of Hypergraph Laplacian and Approximation Algorithms
Journal of the ACM (JACM), Volume 65, Issue 3Article No.: 15, Pages 1–48https://doi.org/10.1145/3178123The celebrated Cheeger’s Inequality (Alon and Milman 1985; Alon 1986) establishes a bound on the edge expansion of a graph via its spectrum. This inequality is central to a rich spectral theory of graphs, based on studying the eigenvalues and ...
- research-articleMarch 2016
Local Computation: Lower and Upper Bounds
Journal of the ACM (JACM), Volume 63, Issue 2Article No.: 17, Pages 1–44https://doi.org/10.1145/2742012The question of what can be computed, and how efficiently, is at the core of computer science. Not surprisingly, in distributed systems and networking research, an equally fundamental question is what can be computed in a distributed fashion. More ...
- research-articleNovember 2015
Optimal Euclidean Spanners: Really Short, Thin, and Lanky
Journal of the ACM (JACM), Volume 62, Issue 5Article No.: 35, Pages 1–45https://doi.org/10.1145/2819008The degree, the (hop-)diameter, and the weight are the most basic and well-studied parameters of geometric spanners. In a seminal STOC'95 paper, titled “Euclidean spanners: short, thin and lanky”, Arya et al. [1995] devised a construction of Euclidean (...
- research-articleNovember 2015
Improved Distributed Approximate Matching
Journal of the ACM (JACM), Volume 62, Issue 5Article No.: 38, Pages 1–17https://doi.org/10.1145/2786753We present distributed network algorithms to compute weighted and unweighted matchings with improved approximation ratios and running times. The computational model is a network of processors exchanging O(log n)-bit messages (the CONGEST model). For ...
- research-articleNovember 2015
Subexponential Algorithms for Unique Games and Related Problems
Journal of the ACM (JACM), Volume 62, Issue 5Article No.: 42, Pages 1–25https://doi.org/10.1145/2775105Subexponential time approximation algorithms are presented for the Unique Games and Small-Set Expansion problems. Specifically, for some absolute constant c, the following two algorithms are presented.
(1) An exp(knϵ)-time algorithm that, given as input ...
- research-articleSeptember 2015
Algorithmic Applications of Baur-Strassen’s Theorem: Shortest Cycles, Diameter, and Matchings
Journal of the ACM (JACM), Volume 62, Issue 4Article No.: 28, Pages 1–30https://doi.org/10.1145/2736283Consider a directed or an undirected graph with integral edge weights from the set [-W, W], that does not contain negative weight cycles. In this article, we introduce a general framework for solving problems on such graphs using matrix multiplication. ...
- research-articleJuly 2014
Solving the Weighted Stable Set Problem in Claw-Free Graphs via Decomposition
Journal of the ACM (JACM), Volume 61, Issue 4Article No.: 20, Pages 1–41https://doi.org/10.1145/2629600We propose an algorithm for solving the maximum weighted stable set problem on claw-free graphs that runs in O(|V|(|E| + |V| log|V|))-time, drastically improving the previous best known complexity bound. This algorithm is based on a novel decomposition ...
- research-articleJanuary 2014
Linear-Time Approximation for Maximum Weight Matching
Journal of the ACM (JACM), Volume 61, Issue 1Article No.: 1, Pages 1–23https://doi.org/10.1145/2529989The maximum cardinality and maximum weight matching problems can be solved in Õ(m√n) time, a bound that has resisted improvement despite decades of research. (Here m and n are the number of edges and vertices.) In this article, we demonstrate that this “...
- research-articleSeptember 2013
All-pairs shortest paths in O(n2) time with high probability
Journal of the ACM (JACM), Volume 60, Issue 4Article No.: 26, Pages 1–25https://doi.org/10.1145/2508028.2505988We present an all-pairs shortest path algorithm whose running time on a complete directed graph on n vertices whose edge weights are chosen independently and uniformly at random from [0,1] is O(n2), in expectation and with high probability. This ...
- research-articleMay 2010
An axiomatic approach to personalized ranking systems
Journal of the ACM (JACM), Volume 57, Issue 4Article No.: 26, Pages 1–35https://doi.org/10.1145/1734213.1734220Personalized ranking systems and trust systems are an essential tool for collaboration in a multi-agent environment. In these systems, trust relations between many agents are aggregated to produce a personalized trust rating of the agents. In this ...