Augmenting Outerplanar Graphs to Meet Diameter Requirements

Given an undirected 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 = N P , 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.