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

__Mittagsseminar Talk Information__ | |

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

**Duration**: 30 minutes

**Location**: OAT S15/S16/S17

**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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