Parallel and On-Line Graph Coloring

We discover a surprising connection between graph coloring in two orthogonal paradigms: parallel and on-line computing. We present a randomized on-line coloring algorithm with a performance ratio of O(n= log n), an improvement of p log n factor over the previous best known algorithm of Vishwanathan. Also, from the same principles, we construct a parallel coloring algorithm with the same performance ratio, for the rst such result. As a byproduct, we obtain a parallel approximation for the independent set problem.