Paper Info
Title
The Matching Problem in General Graphs Is in Quasi-NC
Abstract
We show that the perfect matching problem in general graphs is in Quasi-NC. That is, we give a deterministic parallel algorithm which runs in O(log <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> n) time on n <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">O(log2 n)</sup> processors. The result is obtained by a derandomization of the Isolation Lemma for perfect matchings, which was introduced in the classic paper by Mulmuley, Vazirani and Vazirani [1987] to obtain a Randomized NC algorithm.Our proof extends the framework of Fenner, Gurjar and Thierauf [2016], who proved the analogous result in the special case of bipartite graphs. Compared to that setting, several new ingredients are needed due to the significantly more complex structure of perfect matchings in general graphs. In particular, our proof heavily relies on the laminar structure of the faces of the perfect matching polytope.
Year
DOI
Venue
2017
10.1109/FOCS.2017.70
2017 IEEE 58th Annual Symposium on Foundations of Computer Science (FOCS)
Keywords
DocType
Volume
perfect matching,Isolation Lemma,parallel complexity,derandomization
Journal
abs/1704.01929
ISSN
ISBN
Citations 
0272-5428
978-1-5386-3465-3
5
PageRank 
References 
Authors
0.44
26
2
Name
Order
Citations
PageRank
Ola Svensson134936.31
Jakub Tarnawski2166.34