eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2020-08-18
43:1
43:13
10.4230/LIPIcs.MFCS.2020.43
article
Efficient Isolation of Perfect Matching in O(log n) Genus Bipartite Graphs
Gupta, Chetan
1
Sharma, Vimal Raj
1
Tewari, Raghunath
1
Indian Institute of Technology, Kanpur, India
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol170-mfcs2020/LIPIcs.MFCS.2020.43/LIPIcs.MFCS.2020.43.pdf
Logspace computation
High genus
Matching isolation