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Augmenting Outerplanar Graphs to Meet Diameter Requirements
Author(s) -
Ishii Toshimasa
Publication year - 2013
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.21719
Subject(s) - mathematics , combinatorics , constant (computer programming) , outerplanar graph , graph , discrete mathematics , undirected graph , pathwidth , line graph , computer science , programming language
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.