Department of Computer Science | Institute of Theoretical Computer Science | CADMO

Theory of Combinatorial Algorithms

Prof. Emo Welzl

Mittagsseminar (in cooperation with M. Ghaffari, A. Steger and B. Sudakov)

Mittagsseminar Talk Information

Date and Time: Thursday, September 28, 2017, 12:15 pm

Duration: 30 minutes

Location: CAB G51

Speaker: Jakub Tarnawski (EPFL)

Matching is in Quasi-NC

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^3 n) time on n^{O(\log^2 n)} 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. Joint work with Ola Svensson, to appear at FOCS 2017.

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