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What and Who
Title:Planar Graph Perfect Matching is in NC
Speaker:Vijay V. Vazirani
coming from:University of California, Irvine
Speakers Bio:
Event Type:INF Distinguished Lecture Series
Visibility:D1, D2, D3, D4, D5, RG1, SWS, MMCI
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Level:MPI Audience
Date, Time and Location
Date:Monday, 20 August 2018
Duration:60 Minutes
Building:E1 4
Is perfect matching in NC? That is, is there a deterministic fast parallel algorithm for it?

This has been an outstanding open question in theoretical computer science for over three
decades, ever since the discovery of RNC matching algorithms. Within this question, the case
of planar graphs has remained an enigma: On the one hand, counting the number of perfect
matchings is far harder than finding one (the former is #P-complete and the latter is in P), and
on the other, for planar graphs, counting has long been known to be in NC whereas finding
one has resisted a solution.
In this paper, we give an NC algorithm for finding a perfect matching in a planar graph.
Our algorithm uses the above-stated fact about counting matchings in a crucial way. Our main
new idea is an NC algorithm for finding a face of the perfect matching polytope at which W(n)
new conditions, involving constraints of the polytope, are simultaneously satisfied. Several
other ideas are also needed, such as finding a point in the interior of the minimum weight
face of this polytope and finding a balanced tight odd set in NC.

Name(s):Kurt Mehlhorn
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Created:Kurt Mehlhorn/AG1/MPII/DE, 07/02/2018 09:05 AM Last modified:Uwe Brahm/MPII/DE, 07/03/2018 07:01 AM
  • Kurt Mehlhorn, 07/02/2018 09:05 AM -- Created document.