A tight bound for online colouring of disk graphs

Authors:
Ioannis Caragiannis;Aleksei V. Fishkin;Christos Kaklamanis;Evi Papaioannou
Affiliations:
Research Academic Computer Technology Institute and Department of Computer Engineering and Informatics, University of Patras, 26500 Rio, Greece;Max Plank Institut für Informatik, Im Stadtwald, Geb. 46.1, 66123 Saarbrücken, Germany;Research Academic Computer Technology Institute and Department of Computer Engineering and Informatics, University of Patras, 26500 Rio, Greece;Research Academic Computer Technology Institute and Department of Computer Engineering and Informatics, University of Patras, 26500 Rio, Greece
Venue:
Theoretical Computer Science
Year:
2007

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Abstract

We present an improved upper bound on the competitiveness of the online colouring algorithm First-Fit in disk graphs, which are graphs representing overlaps of disks on the plane. We also show that this bound is best possible for deterministic online colouring algorithms that do not use the disk representation of the input graph. We also present a related new lower bound for unit disk graphs.