Weighted connected domination and Steiner trees in distance-hereditary graphs

Abstract

Distance-hereditary graphs are graphs in which every two vertices have the same distance in every connected induced subgraph containing them. This paper studies distance-hereditary graphs from an algorithmic viewpoint. In particular, we present linear-time algorithms for finding a minimum weighted connected dominating set and a minimum vertex-weighted Steiner tree in a distance-hereditary graph. Both problems are NP-complete in general graphs. (C) 1998 Elsevier Science B.V. All rights reserved.