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Brief announcement: local approximability of minimum dominating set on planar graphs

Published: 15 July 2014 Publication History

Abstract

We show that there is no deterministic local algorithm (constant-time distributed graph algorithm) that finds a (7-ε)-approximation of a minimum dominating set on planar graphs, for any positive constant ε. In prior work, the best lower bound on the approximation ratio has been 5-ε; there is also an upper bound of 52.

References

[1]
Andrzej Czygrinow, Michał Hanćkowiak, and Wojciech Wawrzyniak. Fast distributed approximations in planar graphs. In Proc. 22nd International Symposium on Distributed Computing (DISC 2008), volume 5218 of Lecture Notes in Computer Science, pages 78--92. Springer, 2008.hrefhttp://dx.doi.org/10.1007/978--3--540--87779-0_6\nolinkurldoi:10.1007/978--3--540--87779-0_6.
[2]
Mika Göös, Juho Hirvonen, and Jukka Suomela. Lower bounds for local approximation. Journal of the ACM, 60(5):39:1--23, 2013. http://dx.doi.org/10.1145/2528405 http://arxiv.org/abs/1201.6675 arXiv:1201.6675.
[3]
Christoph Lenzen. Synchronization and Symmetry Breaking in Distributed Systems. PhD thesis, ETH Zurich, January 2011.
[4]
Christoph Lenzen, Yvonne Anne Pignolet, and Roger Wattenhofer. Distributed minimum dominating set approximations in restricted families of graphs. Distributed Computing, 26(2):119--137, 2013. http://dx.doi.org/10.1007/s00446-013-0186-z
[5]
Frank P. Ramsey. On a problem of formal logic. Proceedings of the London Mathematical Society, 30:264--286, 1930. http://dx.doi.org/10.1112/plms/s2--30.1.264
[6]
Jukka Suomela. Survey of local algorithms. ACM Computing Surveys, 45(2):24:1--40, 2013. http://dx.doi.org/10.1145/2431211.2431223 http://www.cs.helsinki.fi/local-survey/.
[7]
Wojciech Wawrzyniak. Brief announcement: a local approximation algorithm for MDS problem in anonymous planar networks. In Proc. 32nd Annual ACM Symposium on Principles of Distributed Computing (PODC 2013), pages 406--408. ACM Press, 2013. http://dx.doi.org/10.1145/2484239.2484281
[8]
Wojciech Wawrzyniak. A strengthened analysis of a local algorithm for the minimum dominating set problem in planar graphs. Information Processing Letters, 114(3):94--98, 2014. http://dx.doi.org/10.1016/j.ipl.2013.11.008

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  • (2025)Distributed domination on sparse graph classesEuropean Journal of Combinatorics10.1016/j.ejc.2023.103773123(103773)Online publication date: Jan-2025
  • (2024)Tight Bounds for Constant-Round Domination on Graphs of High Girth and Low ExpansionStabilization, Safety, and Security of Distributed Systems10.1007/978-3-031-74498-3_20(277-291)Online publication date: 20-Oct-2024
  • (2023)Local certification of graphs with bounded genusDiscrete Applied Mathematics10.1016/j.dam.2022.10.004325(9-36)Online publication date: Jan-2023
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cover image ACM Conferences
PODC '14: Proceedings of the 2014 ACM symposium on Principles of distributed computing
July 2014
444 pages
ISBN:9781450329446
DOI:10.1145/2611462
Permission to make digital or hard copies of part or all 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 third-party components of this work must be honored. For all other uses, contact the Owner/Author.

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Publication History

Published: 15 July 2014

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Author Tags

  1. approximation algorithm
  2. dominating set problem
  3. local distributed algorithm
  4. lower bound
  5. planar graph

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PODC '14
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PODC '14 Paper Acceptance Rate 39 of 141 submissions, 28%;
Overall Acceptance Rate 740 of 2,477 submissions, 30%

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Cited By

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  • (2025)Distributed domination on sparse graph classesEuropean Journal of Combinatorics10.1016/j.ejc.2023.103773123(103773)Online publication date: Jan-2025
  • (2024)Tight Bounds for Constant-Round Domination on Graphs of High Girth and Low ExpansionStabilization, Safety, and Security of Distributed Systems10.1007/978-3-031-74498-3_20(277-291)Online publication date: 20-Oct-2024
  • (2023)Local certification of graphs with bounded genusDiscrete Applied Mathematics10.1016/j.dam.2022.10.004325(9-36)Online publication date: Jan-2023
  • (2022)Local Planar Domination RevisitedStructural Information and Communication Complexity10.1007/978-3-031-09993-9_9(154-173)Online publication date: 27-Jun-2022
  • (2021)Compact Distributed Certification of Planar GraphsAlgorithmica10.1007/s00453-021-00823-w83:7(2215-2244)Online publication date: 1-Jul-2021
  • (2021)Constant Round Distributed Domination on Graph Classes with Bounded ExpansionStructural Information and Communication Complexity10.1007/978-3-030-79527-6_19(334-351)Online publication date: 28-Jun-2021
  • (2020)Compact Distributed Certification of Planar GraphsProceedings of the 39th Symposium on Principles of Distributed Computing10.1145/3382734.3404505(319-328)Online publication date: 31-Jul-2020
  • (2020)A LOCAL Constant Approximation Factor Algorithm for Minimum Dominating Set of Certain Planar GraphsProceedings of the 32nd ACM Symposium on Parallelism in Algorithms and Architectures10.1145/3350755.3400217(501-502)Online publication date: 6-Jul-2020
  • (2019)Distributed Dominating Set Approximations beyond Planar GraphsACM Transactions on Algorithms10.1145/332617015:3(1-18)Online publication date: 17-Jun-2019
  • (2018)Distributed Domination on Graph Classes of Bounded ExpansionProceedings of the 30th on Symposium on Parallelism in Algorithms and Architectures10.1145/3210377.3210383(143-151)Online publication date: 11-Jul-2018
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