Distributed Half-Integral Matching and Beyond
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A4 Artikkeli konferenssijulkaisussa
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en
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18
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Structural Information and Communication Complexity - 30th International Colloquium, SIROCCO 2023, Proceedings, pp. 339-356, Lecture Notes in Computer Science ; Volume 13892
Abstract
By prior work, it is known that any distributed graph algorithm that finds a maximal matching requires Ω(log∗n) communication rounds, while it is possible to find a maximal fractional matching in O(1) rounds in bounded-degree graphs. However, all prior O(1)-round algorithms for maximal fractional matching use arbitrarily fine-grained fractional values. In particular, none of them is able to find a half-integral solution, using only values from {0,12,1}. We show that the use of fine-grained fractional values is necessary, and moreover we give a complete characterization on exactly how small values are needed: if we consider maximal fractional matching in graphs of maximum degree Δ=2d, and any distributed graph algorithm with round complexity T(Δ) that only depends on Δ and is independent of n, we show that the algorithm has to use fractional values with a denominator at least 2d. We give a new algorithm that shows that this is also sufficient.Description
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Dahal, S & Suomela, J 2023, Distributed Half-Integral Matching and Beyond. in S Rajsbaum, S Rajsbaum, A Balliu, D Olivetti & J J Daymude (eds), Structural Information and Communication Complexity - 30th International Colloquium, SIROCCO 2023, Proceedings. Lecture Notes in Computer Science, vol. 13892, Springer, pp. 339-356, International Colloquium on Structural Information and Communication Complexity, Madrid, Spain, 06/06/2023. https://doi.org/10.1007/978-3-031-32733-9_15