A simple and fast parallel coloring algorithm for distance-hereditary graphs
In the literature, there are quite a few sequential and parallel algorithms to solve problems on distance-hereditary graphs. Two well-known classes of graphs, which contain trees and cographs, belong to distance-hereditary graphs. In this paper, we consider the vertex-coloring problem on distance-hereditary graphs. Let T(d)(\V\, \E\) and P(d)(\V\, \E\) denote the time and processor complexities, respectively, required to construct a decomposition tree representation of a distance-hereditary graph G = (V, E) on a PRAM model M(d). Our algorithm runs in O(T(d)(\V\, \E\) + log \V\) time using O(P(d)(\V\, \E\) + \V\/log\V\) processors on M(d). The best known result for constructing a decomposition tree needs O(log(2)\V\) time using O(\V\ + \E\) processors on a CREW PRAM. If a decomposition tree is provided as input, we solve the problem in O(log \V\) time using O(\V\/log\V\) processors on an EREW PRAM. To the best of our knowledge, there is no parallel algorithm for this problem on distance-hereditary graphs.
algorithms distance-hereditary graphs the vertex-coloring problem pram