Efficient parallel algorithm to compute a doubly perfect elimination ordering of a doubly chordal graph

The class of doubly chordal graphs, which is a subclass of chordal graphs and a superclass of strongly chordal graphs, arises in many application areas. Many NP-complete optimization problems on chordal graphs like domination and Steiner tree can be solved in polynomial time on doubly chordal graphs using doubly perfect elimination ordering of vertices. In this paper, we show that the computation of a doubly perfect elimination ordering in a doubly chordal graph with n vertices and m edges can be done in O(log2n) time using O(n+m) processors on the CRCW PRAM model.