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=NP, whil...

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Vydáno v:Journal of graph theory Ročník 74; číslo 4; s. 392 - 416
Hlavní autor: Ishii, Toshimasa
Médium: Journal Article
Jazyk:angličtina
Vydáno: Hoboken Blackwell Publishing Ltd 01.12.2013
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Témata:
Algorithms
constant factor approximation algorithm
Decision trees
diameter
graph augmentation problem
outerplanar graphs
partial 2-trees
undirected graph
ISSN:0364-9024, 1097-0118
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Shrnutí: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=NP, 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.
Bibliografie:istex:6D44827327797D04192FB30DA0828FE8BEC8CCC1
ark:/67375/WNG-198Q6NQ2-K
ArticleID:JGT21719
An extended abstract of this article was presented at 18th Computing: The Australasian Theory Symposium (CATS 2012), Melbourne, Australia, February 2012, pp. 123-132.
Ministry of Education, Culture, Sports, Science and Technology of Japan
Kayamori Foundation of Informational Science Advancement
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.
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ISSN:0364-9024
1097-0118
DOI:10.1002/jgt.21719