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

Theory of Combinatorial Algorithms

Prof. Emo Welzl and Prof. Bernd Gärtner

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

Mittagsseminar Talk Information

Date and Time: Tuesday, April 05, 2022, 12:15 pm

Duration: 30 minutes

Location: CAB G51

Speaker: Saeed Ilchi

Near-Optimal Distributed Dominating Set in Bounded Arboricity Graphs

We describe a simple deterministic O(epsilon^-1 log Delta) round distributed algorithm for 2(alpha+1)(1+epsilon) approximation of minimum weighted dominating set on graphs with arboricity at most alpha. Here Delta denotes the maximum degree. We also show a lower bound proving that this round complexity is nearly optimal even for the unweighted case, via a reduction from the celebrated KMW lower bound on distributed vertex cover approximation [Kuhn, Moscibroda, and Wattenhofer JACM'16]. Our algorithm improves on all the previous results (that work only for unweighted graphs) including a randomized O(alpha^2) approximation in O(log n) rounds [Lenzen and Wattenhofer DISC'10], a deterministic O(alpha log Delta) approximation in O(log Delta) rounds [Lenzen and Wattenhofer DISC'10], a deterministic O(alpha) approximation in O(log^2 Delta) rounds [implicit in Bansal and Umboh IPL'17 and Kuhn, Moscibroda, and Wattenhofer SODA'06], and a randomized O(alpha) approximation in O(alpha log n) rounds [Morgan, Solomon and Wein DISC'21]. This is a joint work with Michal Dory and Mohsen Ghaffari.

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