An Optimal Parallel Algorithm for Node Ranking of Cographs

A ranking of a graph G is a mapping, p, from the vertices of G to the natural numbers such that for every path between any two vertices u and u, uf II, with p(u) = p(u), there exists at least one vertex w on that path with p(w) > p(u) = p(u). The value p(u) of a vertex u is the rank of vertex II. A ranking is optimal if the largest rank assigned is the smallest among all rankings. The optimal ranking problem on a graph G is the problem of finding an optimal ranking on G. We persent a parallel algorithm which needs O(log n) time and n/ log n processors on the EREW PRAM model for this problem on cographs.