On-line interval graphs coloring — Modification of the First-Fit algorithm and its performance ratio

Abstract

We propose a modification of the First-Fit algorithm in which we forbid the use of the most frequently used color. We provide some lower bound of the performance ratio [Formula: see text] on the family of interval graphs [Formula: see text], where [Formula: see text] denotes the number of used colors by the modified version of the First-Fit algorithm and [Formula: see text] is the number of vertices in the largest complete subgraph in [Formula: see text]. We also compare the modification with the usual First-Fit algorithm on some experimental data.