Dynamic programming on distance-hereditary graphs

In this paper, we define a one-vertex-extension tree for a distance-hereditary graph and show how to build it. We then give a unified approach to designing efficient dynamic programming algorithms for distance-hereditary graphs based upon the one-vertex-extension tree. We give linear time algorithms for the weighted vertex cover and weighted independent domination problems and give an O(n(2)) time algorithm to compute a minimum fill-in and the treewidth for a distance-hereditary graph.