Augmenting Outerplanar Graphs to Meet Diameter Requirements

Given an undirected graph G=(V,E) and an integer D1, we consider the problem of augmenting G by a minimum set of new edges so that the diameter becomes at most D. It is known that no constant factor approximation algorithms to this problem with an arbitrary graph G can be obtained unless P=NP, while the problem with only a few graph classes such as forests is approximable within a constant factor. In this article, we give the first constant factor approximation algorithm to the problem with an outerplanar graph G. We also show that if the target diameter D is even, then the case where G is a partial 2-tree is also approximable within a constant. (C) 2013 Wiley Periodicals, Inc. J. Graph Theory 74: 392-416, 2013