Abstract
In this paper we construct two distributed algorithms for computing approximations of a largest matching and a minimum dominating set in planar graphs on n vertices. The approximation ratio in both cases approaches one with n tending to infinity and the number of synchronous communication rounds is poly-logarithmic in n. Our algorithms are purely deterministic.
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Awerbuch, B., Goldberg, A.V., Luby, M., Plotkin, S.A.: Network Decomposition and Locality in Distributed Computation. In: Proc. 30th IEEE Symp. on Foundations of Computer Science, pp. 364–369 (1989)
Cole, R., Vishkin, U.: Deterministic coin tossing with applications to optimal parallel list ranking. Information and Control 70, 32–53 (1986)
Czygrinow, A., Hańćkowiak, M.: Distributed Algorithm for Better Approximation of the Maximum Matching. In: Warnow, T.J., Zhu, B. (eds.) COCOON 2003. LNCS, vol. 2697, pp. 242–251. Springer, Heidelberg (2003)
Czygrinow, A., Hańćkowiak, M.: Distributed algorithms for weighted problems in sparse graphs. To appear in Journal of Discrete Algorithms (in Press) (Available online September 7, 2005)
Czygrinow, A., Hańćkowiak, M., Szymańska, E.: Distributed algorithm for approximating the maximum matching. Discrete Applied Mathematics 143(1-3), 62–71 (2004)
Czygrinow, A., Hańćkowiak, M., Szymańska, E.: A fast distributed algorithm for approximating the maximum matching. In: Albers, S., Radzik, T. (eds.) ESA 2004. LNCS, vol. 3221, pp. 252–263. Springer, Heidelberg (2004)
Dubhashi, D., Mei, A., Panconesi, A., Radhakrishnan, J., Srinivasan, A.: Fast Distributed Algorithms for (Weakly) Connected Dominating Sets and Linear-Size Skeletons. In: Proc. of the ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 717–724 (2003)
Elkin, M.: An Overview of Distributed Approximation. ACM SIGACT News Distributed Computing Column 35(4) (Whole number 132), 40–57 (2004)
Hakimi, S., Mitchem, J., Schmeichel, E.: Star arboricity of graphs. Discrete Mathematics 149(1-3), 93–98 (1996)
Hańćkowiak, M., Karoński, M., Panconesi, A.: A faster distributed algorithm for computing maximal matching deterministically. In: Proceedings of PODC 1999, the Eighteen Annual ACM SIGACT-SIGOPS Symposium on Principles of Distributed Computing, pp. 219–228 (1999)
Jia, L., Rajaraman, R., Suel, R.: An Efficient Distributed Algorithm for Constructing Small Dominating Sets. In: Proc. of the 20th ACM Symposium on Principles of Distributed Computing (PODC), pp. 33–42 (2001)
Kutten, S., Peleg, D.: Fast distributed construction of k-dominating sets and applications. In: Proceedings of the fourteenth annual ACM symposium on Principles of distributed computing, pp. 238–251 (1995)
Kuhn, F., Wattenhofer, R.: Constant-Time Distributed Dominating Set Approximation. In: 22nd ACM Symposium on the Principles of Distributed Computing (PODC), Boston, Massachusetts, USA (July 2003)
Kuhn, F., Moscibroda, T., Wattenhofer, R.: What Cannot Be Computed Locally! In: Proceedings of 23rd ACM Symposium on the Principles of Distributed Computing (PODC), pp. 300–309 (2004)
Linial, N.: Locality in distributed graph algorithms. SIAM Journal on Computing 21(1), 193–201 (1992)
Luby, M.: A simple parallel algorithm for the maximal independent set problem. SIAM J. Comput. 15(4), 1036–1053 (1986)
Peleg, D.: Distributed Computing: A Locality-Sensitive Approach. SIAM, Philadelphia (2000)
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Czygrinow, A., Hańćkowiak, M., Szymańska, E. (2006). Distributed Approximation Algorithms for Planar Graphs. In: Calamoneri, T., Finocchi, I., Italiano, G.F. (eds) Algorithms and Complexity. CIAC 2006. Lecture Notes in Computer Science, vol 3998. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11758471_29
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DOI: https://doi.org/10.1007/11758471_29
Publisher Name: Springer, Berlin, Heidelberg
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