Department of Computer Science | Institute of Theoretical Computer Science | CADMO

Theory of Combinatorial Algorithms

Prof. Emo Welzl and Prof. Bernd Gärtner

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

Mittagsseminar Talk Information

Date and Time: Tuesday, November 17, 2015, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Luis Barba (Carleton University / Université Libre de Bruxelles)

Dynamic Graph Coloring

In this talk, we study the number of vertex recolorings that an algorithm needs to perform in order to maintain a proper coloring of a $C$-colorable graph undergoing four types of updates: (i) delete an edge; (ii) insert an edge; (iii) delete a vertex and all incident edges; or (iv) insert a vertex with a set of incident edges. We assume that all updates keep the graph $C$-colorable and that $N$ is the maximum number of vertices in the graph at any point in time.

We present two algorithms to maintain an approximation of the optimal coloring that, together, present a trade-off between the number of vertex recolorings and the number of colors used to color the graph: For any $d>0$, the first algorithm maintains a proper $O(C d N^{1/d})$-coloring and recolors at most $O(d)$ vertices per update. The second maintains an $O(C d)$-coloring using $O(dN^{1/d})$ recolorings per update. Both algorithms achieve the same asymptotic performance when $d = \log N$.

Moreover, we show that for any algorithm that maintains a $c$-coloring of a $2$-colorable graph on $N$ vertices, there is a sequence of $m$ updates on a specific graph that forces this algorithm to recolor at least $\Omega(m\cdot N^\frac{2}{c(c-1)})$ vertices.

This is joint work with Jean Cardinal, Matias Korman, Stefan Langerman, André van Renssen, Marcel Roeloffzen and Sander Verdonschot.


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