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We show that for each single crossing graph H, a polynomially bounded weight function for all H-minor free graphs G can be constructed in logspace such that it gives nonzero weights to all the cycles in G. This class of graphs subsumes almost all classes of graphs for which such a weight function is known to be constructed in logspace. As a consequence, we obtain that for the class of H-minor free graphs where H is a single crossing graph, reachability can be solved in UL, and bipartite maximum matching can be solved in SPL, which are small subclasses of the parallel complexity class NC. In the restrictive case of bipartite graphs, our maximum matching result improves upon the recent result of Eppstein and Vazirani (SIAM J. Computing 2021), where they show an NC bound for constructing perfect matching in general single crossing minor free graphs.
|Title of host publication||41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science|
|Subtitle of host publication||FSTTCS 2021, December 15–17, 2021, Virtual Conference|
|Publisher||Schloss Dagstuhl-Leibniz-Zentrum für Informatik|
|Number of pages||16|
|Publication status||Published - 29 Nov 2021|
|MoE publication type||A4 Article in a conference publication|
|Event||IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science - Virtual, Online|
Duration: 15 Dec 2021 → 17 Dec 2021
Conference number: 41
|Name||Leibniz International Proceedings in Informatics (LIPIcs)|
|Publisher||Schloss Dagstuhl –Leibniz Center for Informatics|
|Conference||IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science|
|Period||15/12/2021 → 17/12/2021|
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- 1 Active
Parallel and distributed computing for Bayesian graphical models
Suomela, J., Vahidi, H., Gupta, C. & Hirvonen, J.
04/09/2019 → 30/04/2023
Project: Academy of Finland: Other research funding