Abstract
We give a deterministic distributed approximation algorithm for the maximum matching problem in graphs of bounded arboricity. Specifically, given 0 < ε< 1 and a positive integer a, the algorithm finds a matching of size at least (1 − ε)m(G), where m(G) is the size of the maximum matching in an n-vertex graph G with arboricity at most a. The algorithm runs in O(log* n) rounds in the message passing model and it is the first sublogarithmic algorithm for the problem on such a wide class of graphs. Moreover, the result implies that the known \(\Omega(\sqrt{\log n/\log\log n})\) lower bound on the time complexity for a constant or polylogarithmic approximation does not hold for graphs of bounded arboricity.
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Czygrinow, A., Hańćkowiak, M., Szymańska, E. (2009). Fast Distributed Approximation Algorithm for the Maximum Matching Problem in Bounded Arboricity Graphs. In: Dong, Y., Du, DZ., Ibarra, O. (eds) Algorithms and Computation. ISAAC 2009. Lecture Notes in Computer Science, vol 5878. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10631-6_68
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DOI: https://doi.org/10.1007/978-3-642-10631-6_68
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