On-line coloring of geometric intersection graphs

Authors:
Thomas Erlebach;Jiri Fiala
Affiliations:
ETH Zürich, Computer Engineering and Networks Lab, CH-8092 Zürich, Switzerland;Charles University, Faculty of Mathematics and Physics, Institute for Theoretical Computer Science (ITI), Malostranské nám. 2/25, 118 00, Prague, Czech Republic
Venue:
Computational Geometry: Theory and Applications
Year:
2002

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Abstract

This paper studies on-line coloring of geometric intersection graphs. It is shown that no deterministic on-line algorithm can achieve competitive ratio better than Ω (log n) for disk graphs and for square graphs with n vertices, even if the geometric representation is given as part of the input. Furthermore, it is proved that the standard First-fit heuristic achieves competitive ratio O(logn) for disk graphs and for square graphs and is thus best possible.