Reachability and Matching in Single Crossing Minor Free Graphs

Samir Datta, Chetan Gupta, Rahul Jain, Anish Mukherjee, Vimalraj Sharma, Raghunath Tewari

Research output: Chapter in Book/Report/Conference proceedingConference article in proceedingsScientificpeer-review

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Abstract

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.
Original languageEnglish
Title of host publication41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science
Subtitle of host publicationFSTTCS 2021, December 15–17, 2021, Virtual Conference
PublisherSchloss Dagstuhl - Leibniz-Zentrum für Informatik
Pages1-16
Number of pages16
ISBN (Electronic)978-3-95977-215-0
Publication statusPublished - 29 Nov 2021
MoE publication typeA4 Conference publication
EventIARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science - Virtual, Online
Duration: 15 Dec 202117 Dec 2021
Conference number: 41

Publication series

NameLeibniz International Proceedings in Informatics (LIPIcs)
PublisherSchloss Dagstuhl –Leibniz Center for Informatics
Volume213
ISSN (Electronic)1868-8969

Conference

ConferenceIARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science
Abbreviated titleFSTTCS
CityVirtual, Online
Period15/12/202117/12/2021

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