An extended abstract of this article was presented at 18th Computing: The Australasian Theory Symposium (CATS 2012), Melbourne, Australia, February 2012, pp. 123–132.
Augmenting Outerplanar Graphs to Meet Diameter Requirements†
Version of Record online: 24 JAN 2013
© 2013 Wiley Periodicals, Inc.
Journal of Graph Theory
Volume 74, Issue 4, pages 392–416, December 2013
How to Cite
Ishii, T. (2013), Augmenting Outerplanar Graphs to Meet Diameter Requirements. J. Graph Theory, 74: 392–416. doi: 10.1002/jgt.21719
Contract grant sponsor: Ministry of Education, Culture, Sports, Science and Technology of Japan; Contract grant sponsor: Kayamori Foundation of Informational Science Advancement.
- Issue online: 28 OCT 2013
- Version of Record online: 24 JAN 2013
- Manuscript Revised: 28 NOV 2012
- Manuscript Received: 16 FEB 2012
- Ministry of Education, Culture, Sports, Science and Technology of Japan
- Kayamori Foundation of Informational Science Advancement
- undirected graph;
- graph augmentation problem;
- outerplanar graphs;
- partial 2-trees;
- constant factor approximation algorithm
Given an undirected graph and an integer , 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 , 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.