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A Distributed (2 + ε)-Approximation for Vertex Cover in O(log Δ / ε log log Δ) Rounds

Published: 16 June 2017 Publication History

Abstract

We present a simple deterministic distributed (2 + ϵ)-approximation algorithm for minimum-weight vertex cover, which completes in O(log Δ/ϵlog log Δ) rounds, where Δ is the maximum degree in the graph, for any ϵ > 0 that is at most O(1). For a constant ϵ, this implies a constant approximation in O(log Δ/log log Δ) rounds, which contradicts the lower bound of [KMW10].

References

[1]
Matti Åstrand, Patrik Floréen, Valentin Polishchuk, Joel Rybicki, Jukka Suomela, and Jara Uitto. 2009. A local 2-approximation algorithm for the vertex cover problem. In Proceedings of the 23rd International Symposium on Distributed Computing (DISC’09). 191--205.
[2]
Matti Åstrand and Jukka Suomela. 2010. Fast distributed approximation algorithms for vertex cover and set cover in anonymous networks. In Proceedings of the 22nd Annual ACM Symposium on Parallelism in Algorithms and Architectures (SPAA’10). 294--302.
[3]
Reuven Bar-Yehuda. 2000. One for the price of two: A unified approach for approximating covering problems. Algorithmica 27, 2 (2000), 131--144.
[4]
Reuven Bar-Yehuda and Shimon Even. 1981. A linear-time approximation algorithm for the weighted vertex cover problem. J. Algorithms 2, 2 (1981), 198--203.
[5]
Reuven Bar-Yehuda and Shimon Even. 1985. A local-ratio theorem for approximating the weighted vertex cover problem. North-Holland Mathematics Studies 109 (1985), 27--45.
[6]
Reuven Bar-Yehuda and Dror Rawitz. 2005. On the equivalence between the primal-dual schema and the local ratio technique. SIAM J. Discrete Math. 19, 3 (2005), 762--797.
[7]
Leonid Barenboim, Michael Elkin, Seth Pettie, and Johannes Schneider. 2012. The locality of distributed symmetry breaking. In Proceedings of the 53rd Annual IEEE Symposium on Foundations of Computer Science (FOCS’12). 321--330.
[8]
Leonid Barenboim, Michael Elkin, Seth Pettie, and Johannes Schneider. 2016. The locality of distributed symmetry breaking. J. ACM 63, 3 (2016), 20:1--20:45.
[9]
Yi-Jun Chang, Tsvi Kopelowitz, and Seth Pettie. 2016. An exponential separation between randomized and deterministic complexity in the LOCAL model. In FOCS. IEEE Computer Society, 615--624.
[10]
Richard Cole and Uzi Vishkin. 1986. Deterministic coin tossing with applications to optimal parallel list ranking. Inf. Control 70, 1 (1986), 32--53.
[11]
Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein. 2009. Introduction to Algorithms (3rd ed.). MIT Press.
[12]
M. R. Garey and David S. Johnson. 1979. Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman.
[13]
Mohsen Ghaffari. 2016. An improved distributed algorithm for maximal independent set. In SODA. SIAM, 270--277.
[14]
Mohsen Ghaffari and Hsin-Hao Su. 2017. Distributed degree splitting, edge coloring, and orientations. In SODA. SIAM, 2505--2523.
[15]
Fabrizio Grandoni, Jochen Könemann, and Alessandro Panconesi. 2008a. Distributed weighted vertex cover via maximal matchings. ACM Trans. Algorithms 5, 1 (2008).
[16]
Fabrizio Grandoni, Jochen Könemann, Alessandro Panconesi, and Mauro Sozio. 2008b. A primal-dual bicriteria distributed algorithm for capacitated vertex cover. SIAM J. Comput. 38, 3 (2008), 825--840.
[17]
Michal Hanckowiak, Michal Karonski, and Alessandro Panconesi. 2001. On the distributed complexity of computing maximal matchings. SIAM J. Discrete Math. 15, 1 (2001), 41--57.
[18]
Dorit S. Hochbaum. 1982. Approximation algorithms for the set covering and vertex cover problems. SIAM J. Comput. 11, 3 (1982), 555--556.
[19]
Richard M. Karp. 1972. Reducibility among combinatorial problems. In Proceedings of a Symposium on the Complexity of Computer Computations. 85--103.
[20]
Subhash Khot and Oded Regev. 2008. Vertex cover might be hard to approximate to within 2-epsilon. J. Comput. Syst. Sci. 74, 3 (2008), 335--349.
[21]
Samir Khuller, Uzi Vishkin, and Neal E. Young. 1994. A primal-dual parallel approximation technique applied to weighted set and vertex covers. J. Algorithms 17, 2 (1994), 280--289.
[22]
Christos Koufogiannakis and Neal E. Young. 2011. Distributed algorithms for covering, packing and maximum weighted matching. Distrib. Comput. 24, 1 (2011), 45--63.
[23]
Fabian Kuhn, Thomas Moscibroda, and Roger Wattenhofer. 2004. What cannot be computed locally!. In Proceedings of the 23rd Annual ACM Symposium on Principles of Distributed Computing (PODC’04). 300--309.
[24]
Fabian Kuhn, Thomas Moscibroda, and Roger Wattenhofer. 2006. The price of being near-sighted. In Proceedings of the 17th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA’06). 980--989.
[25]
Fabian Kuhn, Thomas Moscibroda, and Roger Wattenhofer. 2010. Local computation: Lower and upper bounds. CoRR abs/1011.5470 (2010). http://arxiv.org/abs/1011.5470
[26]
Fabian Kuhn, Thomas Moscibroda, and Roger Wattenhofer. 2016. Local computation: Lower and upper bounds. J. ACM 63, 2 (2016), 17:1--17:44.
[27]
George L. Nemhauser and Leslie E. Trotter Jr. 1975. Vertex packings: Structural properties and algorithms. Math. Program. 8, 1 (1975), 232--248.
[28]
Alessandro Panconesi and Romeo Rizzi. 2001. Some simple distributed algorithms for sparse networks. Distrib. Comput. 14, 2 (2001), 97--100.
[29]
Boaz Patt-Shamir, Dror Rawitz, and Gabriel Scalosub. 2012. Distributed approximation of cellular coverage. J. Parallel Distrib. Comput. 72, 3 (2012), 402--408.
[30]
Seth Pettie. 2016. Personal communication.
[31]
Valentin Polishchuk and Jukka Suomela. 2009. A simple local 3-approximation algorithm for vertex cover. Inf. Process. Lett. 109, 12 (2009), 642--645.

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cover image Journal of the ACM
Journal of the ACM  Volume 64, Issue 3
June 2017
294 pages
ISSN:0004-5411
EISSN:1557-735X
DOI:10.1145/3107927
Issue’s Table of Contents
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Association for Computing Machinery

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Publication History

Published: 16 June 2017
Accepted: 01 February 2017
Received: 01 September 2016
Published in JACM Volume 64, Issue 3

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Author Tags

  1. Distributed computing
  2. approximation algorithms
  3. graph algorithms
  4. local-ratio
  5. vertex cover

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  • Israel Science Foundation

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  • (2024)Distributed Fractional Local Ratio and Independent Set ApproximationInformation and Computation10.1016/j.ic.2024.105238(105238)Online publication date: Nov-2024
  • (2024)Distributed Fractional Local Ratio and Independent Set ApproximationStructural Information and Communication Complexity10.1007/978-3-031-60603-8_16(281-299)Online publication date: 23-May-2024
  • (2023)Computing Connected-k-Subgraph Cover with Connectivity RequirementTheory and Applications of Models of Computation10.1007/978-3-031-20350-3_9(93-102)Online publication date: 1-Jan-2023
  • (2022)Better Approximation for Distributed Weighted Vertex Cover via Game-Theoretic LearningIEEE Transactions on Systems, Man, and Cybernetics: Systems10.1109/TSMC.2021.312169552:8(5308-5319)Online publication date: Aug-2022
  • (2022)A localized distributed algorithm for vertex cover problemJournal of Computational Science10.1016/j.jocs.2021.10151858(101518)Online publication date: Feb-2022
  • (2021)A Minimal Memory Game-based Distributed Algorithm to Vertex Cover of Networks2021 IEEE International Symposium on Circuits and Systems (ISCAS)10.1109/ISCAS51556.2021.9401117(1-5)Online publication date: May-2021
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  • (2019)A Time Hierarchy Theorem for the LOCAL ModelSIAM Journal on Computing10.1137/17M115795748:1(33-69)Online publication date: 3-Jan-2019
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