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Efficient Isolation of Perfect Matching in O(log n) Genus Bipartite Graphs Gupta, Chetan Sharma, Vimal Raj Tewari, Raghunath Logspace computation High genus Matching isolation We show that given an embedding of an O(log n) genus bipartite graph, one can construct an edge weight function in logarithmic space, with respect to which the minimum weight perfect matching in the graph is unique, if one exists. As a consequence, we obtain that deciding whether such a graph has a perfect matching or not is in SPL. In 1999, Reinhardt, Allender and Zhou proved that if one can construct a polynomially bounded weight function for a graph in logspace such that it isolates a minimum weight perfect matching in the graph, then the perfect matching problem can be solved in SPL. In this paper, we give a deterministic logspace construction of such a weight function for O(log n) genus bipartite graphs. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Chetan Gupta and Vimal Raj Sharma and Raghunath Tewari 2020 Is Part Of LIPIcs, Volume 170, 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.MFCS.2020.43 urn:nbn:de:0030-drops-127099 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2020.43 eng https://creativecommons.org/licenses/by/3.0/legalcode