Augmenting Outerplanar Graphs to Meet Diameter Requirements


  • An extended abstract of this article was presented at 18th Computing: The Australasian Theory Symposium (CATS 2012), Melbourne, Australia, February 2012, pp. 123–132.

  • Contract grant sponsor: Ministry of Education, Culture, Sports, Science and Technology of Japan; Contract grant sponsor: Kayamori Foundation of Informational Science Advancement.


Given an undirected graph math formula and an integer math formula, 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 math formula, 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.