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

Date and Time: Tuesday, May 08, 2007, 12:15 pm

Duration: This information is not available in the database

Location: OAT S15/S16/S17

Speaker: Fabian Kuhn

On the Complexity of Distributed Graph Coloring

Coloring the nodes of a graph with a small number of colors is one of the most fundamental problems in theoretical computer science. We study graph coloring in a distributed setting. Processors of a distributed system are nodes of an undirected graph G. There is an edge between two nodes whenever the corresponding processors can directly communicate with each other. We assume that distributed coloring algorithms start with an initial m-coloring of G. We prove new lower bounds for two special kinds of coloring algorithms. For algorithms which run for a single communication round---i.e., every node of the network can only send its initial color to all its neighbors---, we show that the number of colors of the computed coloring has to be at least Omega(Delta^2/log^2(Delta)+loglog m) where Delta is the largest degree of G. It is known that it is possible to color G with O(Delta^2*log m) colors in one round. If such one-round algorithms are iteratively applied to reduce the number of colors step-by-step, we prove a time lower bound of Omega(Delta/log^2(Delta)+log^*m) to obtain an O(Delta)-coloring where the best known upper bound are O(Delta*log(Delta)+log^*m) rounds. The best previous lower bounds for the two types of algorithms are Omega(loglog m) colors and Omega(log^*m) rounds, respectively.

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

Previous talks by year:   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