Augmenting Outerplanar Graphs to Meet Diameter Requirements

Given a graph G = (V, E) and an integer D ≥ 1, 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 paper, 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.