In the literature, there are quite a few sequential and parallel algorithms to solve problems in a distance-hereditary graph G utilizing techniques discovered from the properties of the problems. Based on structural properties of G, we first sketch characteristics of problems which can be systematic solved on G and then define a general problem-solving paradigm. Given a decomposition tree representation of G, we propose a unified approach to construct sequential dynamic-programming algorithms for several fundamental graph-theoretical problems that fit into our paradigm. We also show that our sequential solutions can be efficiently parallelized using the tree contraction technique.
