Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Date and Time: Thursday, October 10, 2019, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Vaclav Rozhon

Distributed Derandomization via Network Decomposition

We present a simple polylogarithmic-time deterministic distributed algorithm for network decomposition. This improves on a celebrated exponentially slower algorithm of Panconesi and Srinivasan [STOC'93] and settles one of the long-standing and central questions in distributed graph algorithms. It also leads to the first polylogarithmic-time deterministic distributed algorithms for numerous other graph problems, hence resolving several open problems, including Linial's well-known question about the deterministic complexity of maximal independent set [FOCS'87].

Put together with the results of Ghaffari, Kuhn, and Maus [STOC'17] and Ghaffari, Harris, and Kuhn [FOCS'18], we get a general distributed derandomization result that implies P-RLOCAL = P-LOCAL. That is, for any distributed problem whose solution can be checked in polylogarithmic-time, any polylogarithmic-time randomized algorithm can be derandomized to a polylogarithmic-time deterministic algorithm.

By known connections, our result leads also to substantially faster randomized algorithms for a number of fundamental problems including (Δ+1)-coloring, MIS, and Lovász Local Lemma.

Joint work with Mohsen Ghaffari

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