On the performance of the first-fit coloring algorithm on permutation graphs

In this paper we study the performance of a particular on-line coloring algorithm, the First-Fit or Greedy algorithm, on a class of perfect graphs namely the permutation graphs. We prove that the largest number of colors FF(G) that the First-Fit coloring algorithm (FF) needs on permutation graphs of chromatic number (G) = when taken over all possible vertex orderings is not linearly bounded in terms of the off-line optimum, if is a fixed positive integer. Specifically, we prove that for any integers > 0 and k 0, there exists a permutation graph G on n vertices such that (G) = and FF(G) 1 2 ((2 +)+k(2 -)), for sufficiently large n. Our result shows that the class of permutation graphs P is not First-Fit -bounded; that is, there exists no function f such that for all graphs G P, FF(G) f ((G)). Recall that for perfect graphs (G) = (G), where (G) denotes the clique number of G.

• Type: Journal
• Year: 2000
• Where: IPL
• Authors: Stavros D. Nikolopoulos, Charis Papadopoulos
• Keywords: IPL 2000, On-line Coloring Algorithm, Perfect Graphs, Permutation Graphs