Some optimal parallel algorithms on weighted cographs

The class of cographs, or complement-reducible graphs, arises naturally in many different areas of applied mathematics and computer science. In this paper we present an O(n) time sequential algorithm and a parallel algorithm of O(log n) time and O(n/log n) processors on the EREW PRAM model to solve the maximum weight independent set problem on weighted cographs. Using such algorithms we can easily solve the minimum weight vertex cover, maximum weight clique, minimum weight independent dominating set, minimum weight dominating set, and minimum weight maximal irredundant set problems on weighted cographs with the same bounds of time and processors.