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

__Mittagsseminar Talk Information__ | |

**Date and Time**: Thursday, September 21, 2017, 12:15 pm

**Duration**: 30 minutes

**Location**: CAB G51

**Speaker**: Manuela Fischer

## Deterministic Distributed Edge-Coloring via Hypergraph Maximal Matching

We present a deterministic distributed algorithm that computes a $(2\Delta−1)$-edge-coloring, or even list-edge-coloring, in any n-node graph with maximum degree $\Delta$, in $O(\log^8\Delta \log n)$ rounds. This answers one of the long-standing open questions of distributed graph algorithms from the late 1980s, which asked for a polylogarithmic-time algorithm. See, e.g., Open Problem 4 in the Distributed Graph Coloring book of Barenboim and Elkin. The previous best round complexities were $2^{O(\sqrt{\log n})}$ by Panconesi and Srinivasan [STOC'92] and $\tilde{O}(\sqrt{\Delta})+O(log^*n)$ by Fraigniaud, Heinrich, and Kosowski [FOCS'16].

A corollary of our deterministic list-edge-coloring also improves the randomized complexity of $(2\Delta−1)$-edge-coloring to $poly(\log\log n)$ rounds.

The key technical ingredient is a deterministic distributed algorithm for hypergraph maximal matching, which we believe will be of interest beyond this result. In any hypergraph of rank r --- where each hyperedge has at most r vertices --- with n nodes and maximum degree $\Delta$, this algorithm computes a maximal matching in $O(r^5 \log^{6+\log r} \Delta \log n)$ rounds.

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

Previous talks by year: 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