Mittagsseminar (in cooperation with J. Lengler, A. Steger, and D. Steurer)

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

Duration: 30 minutes

Location: OAT S15/S16/S17

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:   2025  2024  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