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Parallel Set Cover and Hypergraph Matching via Uniform Random Sampling

Authors Laxman Dhulipala, Michael Dinitz , Jakub Łącki , Slobodan Mitrović

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Author Details

Laxman Dhulipala
  • Google Research, New York, NY, USA
Michael Dinitz
  • Johns Hopkins University, Baltimore, MD, USA
Jakub Łącki
  • Google Research, New York, NY, USA
Slobodan Mitrović
  • UC Davis, CA, USA

Funding

  • Dinitz, Michael: Supported in part by NSF awards CCF-1909111 and CCF-2228995.
  • Mitrović, Slobodan: Supported by the Google Research Scholar and NSF Faculty Early Career Development Program No. 2340048.

Cite AsGet BibTex

Laxman Dhulipala, Michael Dinitz, Jakub Łącki, and Slobodan Mitrović. Parallel Set Cover and Hypergraph Matching via Uniform Random Sampling. In 38th International Symposium on Distributed Computing (DISC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 319, pp. 19:1-19:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.DISC.2024.19

Abstract

The SetCover problem has been extensively studied in many different models of computation, including parallel and distributed settings. From an approximation point of view, there are two standard guarantees: an O(log Δ)-approximation (where Δ is the maximum set size) and an O(f)-approximation (where f is the maximum number of sets containing any given element). In this paper, we introduce a new, surprisingly simple, model-independent approach to solving SetCover in unweighted graphs. We obtain multiple improved algorithms in the MPC and CRCW PRAM models. First, in the MPC model with sublinear space per machine, our algorithms can compute an O(f) approximation to SetCover in Ô(√{log Δ} + log f) rounds and a O(log Δ) approximation in O(log^{3/2} n) rounds. Moreover, in the PRAM model, we give a O(f) approximate algorithm using linear work and O(log n) depth. All these bounds improve the existing round complexity/depth bounds by a log^{Ω(1)} n factor. Moreover, our approach leads to many other new algorithms, including improved algorithms for the HypergraphMatching problem in the MPC model, as well as simpler SetCover algorithms that match the existing bounds.

Subject Classification

ACM Subject Classification
  • Theory of computation → Massively parallel algorithms
  • Theory of computation → Shared memory algorithms
  • Theory of computation → MapReduce algorithms
Keywords
  • approximate maximum matching
  • set cover
  • hypergraph matching
  • PRAM
  • massively parallel computation

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