A parallel variant of a heuristical algorithm for graph coloring — Corrigendum

Abstract

In the paper [2] a randomized algorithm of Petford and Welsh [1] was parallelized and optimal speedup as well as linear time complexity was reported. Later, an error was found in the simulation program when the experiments were repeated independently. Consequently, Table 1 of [2] is incorrect. Here we explain how the parallelization has to be modified to ge essentially (up to a constant factor) the same results: the linear average time complexity of the parallel variant of the algorithm and optimal speedup. In the first section we give the corrected algorithm. An example which gives some idea of what kind of problems can arise in a straightforward implementation follows. We conclude with experimental result of the corrected algorithm.