A polynomial-time algorithm for Outerplanar Diameter Improvement

The Outerplanar Diameter Improvement problem asks, given a graph G and an integer D, whether it is possible to add edges to G in a way that the resulting graph is outerplanar and has diameter at most D. We provide a dynamic programming algorithm that solves this problem in polynomial time. Outerplan...

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Bibliographic Details
Published in:Journal of computer and system sciences Vol. 89; pp. 315 - 327
Main Authors: Cohen, Nathann, Gonçalves, Daniel, Kim, Eun Jung, Paul, Christophe, Sau, Ignasi, Thilikos, Dimitrios M., Weller, Mathias
Format: Journal Article
Language:English
Published: Elsevier Inc 01.11.2017
Elsevier
Subjects:
Combinatorics
Completion problems
Computational Complexity
Computer Science
Data Structures and Algorithms
Diameter improvement
Dynamic programming
Mathematics
Outerplanar graphs
Polynomial-time algorithms
Diameter improvement
Outerplanar graphs
Polynomial-time algorithms
Completion problems
Dynamic programming
ISSN:0022-0000, 1090-2724
Online Access:Get full text
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Summary:The Outerplanar Diameter Improvement problem asks, given a graph G and an integer D, whether it is possible to add edges to G in a way that the resulting graph is outerplanar and has diameter at most D. We provide a dynamic programming algorithm that solves this problem in polynomial time. Outerplanar Diameter Improvement demonstrates several structural analogues to the celebrated and challenging Planar Diameter Improvement problem, where the resulting graph should, instead, be planar. The complexity status of this latter problem is open. •The goal of Outerplanar Diameter Improvement is to add edges to a graph G to obtain an outerplanar graph of diameter at most D.•We provide a dynamic programming algorithm that solves the problem in polynomial time.•This problem has structural analogues to the open problem Planar Diameter Improvement, where the resulting graph should be planar.
ISSN:0022-0000
1090-2724
DOI:10.1016/j.jcss.2017.05.016