Fast parallel algorithms for cographs

Abstract

In this paper we propose a new way of looking at cographs and show how it affords us a fast parallel recognition algorithm. Additionally, should the graph under investigation be a cograph, our algorithm constructs its unique tree representation. Next, given a cograph along with its tree representation we obtain a fast parallel coloring algorithm. Specifically, for a graph G with n vertices and m edges as input, our parallel recognition algorithm runs in O(logn) EREW time using $O(\frac{{n^2 + mn}}{{\log n}})$ processors. Once the cotree of a cograph is available, our coloring algorithm runs in O(log n) EREW time using $O(\frac{n}{{\log n}})$ processors.

This work was supported by the National Science Foundation under grant CCR-8909996.