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

__Mittagsseminar Talk Information__ | |

**Date and Time**: Thursday, April 29, 2021, 12:15 pm

**Duration**: 30 minutes

**Location**: Zoom: conference room

**Speaker**: Sebastian Brandt

## Improved Distributed Lower Bounds for MIS and Bounded Degree Dominating Sets on Trees

Given a graph G = (V,E) and a parameter k, a k-degree dominating set is a subset S of V such that S is a dominating set of G and in the induced subgraph G[S] every node has degree at most k. For k = 0, this definition coincides with the definition of a maximal independent set (MIS), while for k > 0, the problem of finding a k-degree dominating set is a natural relaxation of the MIS problem. Due to work by Barenboim and Elkin [PODC'08] and Ghaffari [SODA'16], it is known that, on trees, an MIS, and therefore also a k-degree dominating set for any k, can be computed in O(log n / log log n) rounds deterministically, and in O(sqrt(log n)) rounds randomized, in the distributed LOCAL model.

In this talk, we present Omega(sqrt(log n))-round lower bounds for the deterministic, and Omega(sqrt(log log n))-round lower bounds for the randomized computation of k-degree dominating sets on trees, both in the LOCAL model, improving, for k > 0, on the best previously known lower bounds of Omega(log*n)) due to Linial [FOCS'87] and Naor [J.Disc.Math.'91]. Our results also slightly improve on the best previously known lower bounds for MIS on trees due to Balliu, Brandt, and Olivetti [FOCS'20], while providing a simpler proof.

This is joint work with Alkida Balliu, Fabian Kuhn, and Dennis Olivetti.

Upcoming talks | All previous talks | Talks by speaker | Upcoming talks in iCal format (beta version!)

Previous talks by year: 2023 2022 2021 2020 2019 2018 2017 2016 2015 2014 2013 2012 2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001 2000 1999 1998 1997 1996

Information for students and suggested topics for student talks

Automatic MiSe System Software Version 1.4803M | admin login