Abstract
A coloring of a graph G is an assignment of colors to the vertices of G so that adjacent vertices are assigned distinct colors. The coloring problem is to color an input graph with the minimum number of colors. This problem is a well-known NP-complete problem, However, it can be solved in polynomial time for certain classes of graphs, e.g., interval graphs, permutation graphs and trapezoid graphs. Coloring algorithms for these graphs have applications to wire routing problems for integrated circuits. In this paper, we propose a parallel algorithm for solving the coloring problem on trapezoid graphs G which runs in O( log 2 n) time using O( n 3 log n ) processors on the CREW PRAM where n is the number of vertices of G.
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