On Lower Bounds for the Time and the Bit Complexity of Some Probabilistic Distributed Graph Algorithms
(Extended Abstract)
Conference paper
- 1.2k Downloads
Abstract
This paper concerns probabilistic distributed graph algorithms to solve classical graph problems such as colouring, maximal matching or maximal independent set. We consider anonymous networks (no unique identifiers are available) where vertices communicate by single bit messages. We present a general framework, based on coverings, for proving lower bounds for the bit complexity and thus the execution time to solve these problems. In this way we obtain new proofs of some well known results and some new ones.
Keywords
Connected Graph Maximal Match Label Graph Port Numbering Election Algorithm
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Preview
Unable to display preview. Download preview PDF.
References
- [Ang80]Angluin, D.: Local and global properties in networks of processors. In: Proceedings of the 12th Symposium on Theory of Computing, pp. 82–93 (1980)Google Scholar
- [BMW94]Bodlaender, H.L., Moran, S., Warmuth, M.K.: The distributed bit complexity of the ring: from the anonymous case to the non-anonymous case. Information and Computation 114(2), 34–50 (1994)CrossRefMathSciNetGoogle Scholar
- [Bod89]Bodlaender, H.-L.: The classification of coverings of processor networks. J. Parallel Distrib. Comput. 6, 166–182 (1989)CrossRefGoogle Scholar
- [BV02]Boldi, P., Vigna, S.: Fibrations of graphs. Discrete Math. 243, 21–66 (2002)CrossRefzbMATHMathSciNetGoogle Scholar
- [CM07]Chalopin, J., Métivier, Y.: An efficient message passing election algorithm based on Mazurkiewicz’s algorithm. Fundam. Inform. 80(1-3), 221–246 (2007)zbMATHGoogle Scholar
- [DMR08]Dinitz, Y., Moran, S., Rajsbaum, S.: Bit complexity of breaking and achieving symmetry in chains and rings. Journal of the ACM 55(1) (2008)Google Scholar
- [FMRZar]Fontaine, A., Métivier, Y., Robson, J.M., Zemmari, A.: The bit complexity of the MIS problem and of the maximal matching problem in anonymous rings. Information and Computation (to appear)Google Scholar
- [II86]Israeli, A., Itai, A.: A fast and simple randomized parallel algorithm for maximal matching. Information Processing Letters 22, 77–80 (1986)CrossRefMathSciNetGoogle Scholar
- [KN99]Kushilevitz, E., Nisan, N.: Communication complexity. Cambridge University Press (1999)Google Scholar
- [KOSS06]Kothapalli, K., Onus, M., Scheideler, C., Schindelhauer, C.: Distributed coloring in \({O}(\sqrt{\log n})\) bit rounds. In: Proceedings of the 20th International Parallel and Distributed Processing Symposium (IPDPS 2006), Rhodes Island, Greece, April 25-29. IEEE (2006)Google Scholar
- [MRSDZ10]Métivier, Y., Robson, J.M., Saheb-Djahromi, N., Zemmari, A.: About randomised distributed graph colouring and graph partition algorithms. Information and Computation 208(11), 1296–1304 (2010)CrossRefzbMATHMathSciNetGoogle Scholar
- [MRSDZ11]Métivier, Y., Robson, J.M., Saheb-Djahromi, N., Zemmari, A.: An optimal bit complexity randomized distributed MIS algorithm. Distributed Computing 23(5-6), 331–340 (2011)CrossRefzbMATHGoogle Scholar
- [Rei32]Reidemeister, K.: Einführung in die Kombinatorische Topologie. Vieweg, Brunswick (1932)Google Scholar
- [Tel00]Tel, G.: Introduction to distributed algorithms. Cambridge University Press (2000)Google Scholar
- [Yao79]Yao, A.C.: Some complexity questions related to distributed computing. In: Proceedings of the 11th ACM Symposium on Theory of Computing (STOC), pp. 209–213. ACM Press (1979)Google Scholar
Copyright information
© Springer International Publishing Switzerland 2014