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Keywords:

  • undirected graph;
  • graph augmentation problem;
  • diameter;
  • outerplanar graphs;
  • partial 2-trees;
  • constant factor approximation algorithm

Abstract

Given an undirected graph inline image and an integer inline image, 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 inline image, 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.