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Constant Round Distributed Domination on Graph Classes with Bounded Expansion

Published: 28 June 2021 Publication History

Abstract

We show that the dominating set problem admits a constant factor approximation in a constant number of rounds in the LOCAL model of distributed computing on graph classes with bounded expansion. This generalizes a result of Czygrinow et al. for graphs with excluded topological minors.

References

[1]
Akhoondian Amiri, S., Ossona de Mendez, P., Rabinovich, R., Siebertz, S.: Distributed domination on graph classes of bounded expansion. In: Proceedings of the 30th on Symposium on Parallelism in Algorithms and Architectures, pp. 143–151 (2018)
[2]
Akhoondian Amiri, S., Schmid, S., Siebertz, S.: A local constant factor MDS approximation for bounded genus graphs. In: Proceedings of the 2016 ACM Symposium on Principles of Distributed Computing, pp. 227–233 (2016)
[3]
Amiri, S.A., Schmid, S.: Brief announcement: a log*-time local MDS approximation scheme for bounded genus graphs. In: Proceedings of DISC (2016)
[4]
Amiri SA, Schmid S, and Siebertz S Distributed dominating set approximations beyond planar graphs ACM Trans. Algorithms (TALG) 2019 15 3 1-18
[5]
Bansal N and Umboh SW Tight approximation bounds for dominating set on graphs of bounded arboricity Inf. Process. Lett 2017 122 21-24
[6]
Barenboim L, Elkin M, and Gavoille C A fast network-decomposition algorithm and its applications to constant-time distributed computation Theoret. Comput. Sci. 2018 751 2-23
[7]
Brönnimann H and Goodrich MT Almost optimal set covers in finite VC-dimension Discrete Comput. Geom. 1995 14 4 463-479
[8]
Czygrinow A, Hańćkowiak M, and Wawrzyniak W Taubenfeld G Fast distributed approximations in planar graphs Distributed Computing 2008 Heidelberg Springer 78-92
[9]
Czygrinow, A., Hanckowiak, M., Wawrzyniak, W., Witkowski, M.: Distributed approximation algorithms for the minimum dominating set in k_h-minor-free graphs. In: 29th International Symposium on Algorithms and Computation (ISAAC 2018). Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik (2018)
[10]
Dinur, I., Steurer, D.: Analytical approach to parallel repetition. In: Proceedings of the Forty-Sixth Annual ACM Symposium on Theory of Computing, pp. 624–633 (2014)
[11]
Drange, P.G., et al.: Kernelization and sparseness: the case of dominating set. In: 33rd Symposium on Theoretical Aspects of Computer Science, STACS 2016, pp. 31:1–31:14 (2016)
[12]
Eiben E, Kumar M, Mouawad AE, Panolan F, and Siebertz S Lossy kernels for connected dominating set on sparse graphs SIAM J. Discrete Math. 2019 33 3 1743-1771
[13]
Eickmeyer, K., et al.: Neighborhood complexity and kernelization for nowhere dense classes of graphs. In: 44th International Colloquium on Automata, Languages, and Programming, ICALP 2017, 10–14 July 2017, Warsaw, Poland, pp. 63:1–63:14 (2017)
[14]
Even G, Rawitz D, and Shahar SM Hitting sets when the VC-dimension is small Inf. Process. Lett. 2005 95 2 358-362
[15]
Fabianski, G., Pilipczuk, M., Siebertz, S., Torunczyk, S.: Progressive algorithms for domination and independence. In: 36th International Symposium on Theoretical Aspects of Computer Science, STACS 2019, 13–16 March 2019, Berlin, Germany, pp. 27:1–27:16 (2019)
[16]
Gallager RG, Humblet PA, and Spira PM A distributed algorithm for minimum-weight spanning trees ACM Trans. Program. Langu. Syst. (TOPLAS) 1983 5 1 66-77
[17]
Garey, M.R., Johnson, D.S.: Computers and Intractability, vol. 174. Freeman San Francisco (1979)
[18]
Ghaffari, M., Kuhn, F., Maus, Y.: On the complexity of local distributed graph problems. In: STOC, pp. 784–797. ACM (2017)
[19]
Har-Peled S and Quanrud K Approximation algorithms for polynomial-expansion and low-density graphs SIAM J. Comput. 2017 46 6 1712-1744
[20]
Hilke, M., Lenzen, C., Suomela, J.: Brief announcement: local approximability of minimum dominating set on planar graphs. In: Proceedings of the 2014 ACM Symposium on Principles of Distributed Computing, pp. 344–346 (2014)
[21]
Johnson DS Approximation algorithms for combinatorial problems J. Comput. Syst. Sci. 1974 9 3 256-278
[22]
Jones M, Lokshtanov D, Ramanujan M, Saurabh S, and Suchý O Parameterized complexity of directed Steiner tree on sparse graphs SIAM J. Discrete Math. 2017 31 2 1294-1327
[23]
Karp, R.M.: Reducibility among combinatorial problems. In: Miller, R.E., Thatcher, J.W., Bohlinger, J.D. (eds.) Complexity of Computer Computations, pp. 85–103. Springer, Boston (1972).
[24]
Kreutzer S, Rabinovich R, and Siebertz S Polynomial kernels and wideness properties of nowhere dense graph classes ACM Trans. Algorithms (TALG) 2018 15 2 1-19
[25]
Kuhn, F., Moscibroda, T., Wattenhofer, R.: Local computation: lower and upper bounds. J. ACM 63(2), 17:1–17:44 (2016)
[26]
Lenzen C, Pignolet YA, and Wattenhofer R Distributed minimum dominating set approximations in restricted families of graphs Distrib. Comput. 2013 26 2 119-137
[27]
Lenzen C and Wattenhofer R Taubenfeld G Leveraging Linial’s locality limit Distributed Computing 2008 Heidelberg Springer 394-407
[28]
Lenzen C and Wattenhofer R Lynch NA and Shvartsman AA Minimum dominating set approximation in graphs of bounded arboricity Distributed Computing 2010 Heidelberg Springer 510-524
[29]
Lovász L On the ratio of optimal integral and fractional covers Discrete Math. 1975 13 4 383-390
[30]
Nešetřil, J., de Mendez, P.O.: Grad and classes with bounded expansion I. decompositions. Eur. J. Comb. 29(3), 760–776 (2008)
[31]
Nešetřil J, de Mendez PO, and Wood DR Characterisations and examples of graph classes with bounded expansion Eur. J. Comb. 2012 33 3 350-373
[32]
Rozhon, V., Ghaffari, M.: Polylogarithmic-time deterministic network decomposition and distributed derandomization. In: STOC, pp. 350–363. ACM (2020)
[33]
Siebertz S Greedy domination on biclique-free graphs Inf. Process. Lett. 2019 145 64-67
[34]
Wawrzyniak, W.: Brief announcement: a local approximation algorithm for MDS problem in anonymous planar networks. In: Proceedings of the 2013 ACM Symposium on Principles of Distributed Computing, pp. 406–408 (2013)
[35]
Wawrzyniak W A strengthened analysis of a local algorithm for the minimum dominating set problem in planar graphs Inf. Process. Lett. 2014 114 3 94-98

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cover image Guide Proceedings
Structural Information and Communication Complexity: 28th International Colloquium, SIROCCO 2021, Wrocław, Poland, June 28 – July 1, 2021, Proceedings
Jun 2021
395 pages
ISBN:978-3-030-79526-9
DOI:10.1007/978-3-030-79527-6

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Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 28 June 2021

Author Tags

  1. Dominating set
  2. LOCAL algorithm
  3. Bounded expansion graph classes

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