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

Date and Time: Tuesday, September 29, 2020, 12:15 pm

Duration: 30 minutes

Location: Zoom: conference room

Speaker: Christoph Grunau

Improved Deterministic Network Decomposition

Network decomposition is a central tool in distributed graph algorithms. In a recent breakthrough, Rozhoň and Ghaffari presented the first deterministic LOCAL algorithm for network decomposition running in a polylogarithmic number of rounds [STOC'20]. This O(log^7 n)-round algorithm was the first improvement since the exponentially slower algorithm of Panconesi and Srinivasan [STOC'93]. Currently, the best-known deterministic and randomized algorithms for a variety of problems in the LOCAL model, including MIS and (Δ+1)-coloring, use network decomposition as a subroutine. Hence, an improved round complexity for network decomposition directly translates to improved round complexities for various deterministic and randomized algorithms in the LOCAL model. In this talk, we build and improve upon the network decomposition algorithm of Rozhoň and Ghaffari to obtain a deterministic network decomposition algorithm with a round complexity of O(log^5 n). This is joint work with Mohsen Ghaffari and Vasek Rozhoň.

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