The parametric complexity of graph diameter augmentation

The diameter of a graph is the maximum distance between any pair of vertices in the graph. The Diameter-tAugmentation problem takes as input a graph G=(V,E) and a positive integer k and asks whether there exists a set E2 of at most k new edges so that the graph G2=(V,E∪E2) has diameter t. This probl...

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Bibliographic Details
Published inDiscrete Applied Mathematics Vol. 161; no. 10-11; pp. 1626 - 1631
Main Authors Gao, Yong, Hare, Donovan R., Nastos, James
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.07.2013
Subjects
[formula omitted]-hard
Augmentation
Complexity
Fixed-parameter tractability
Graph augmentation
Graph diameter
Graphs
Integers
Lithium
Mathematical analysis
Reduction
Graph diameter
W-hard
Reduction
Fixed-parameter tractability
Graph augmentation
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Summary:The diameter of a graph is the maximum distance between any pair of vertices in the graph. The Diameter-tAugmentation problem takes as input a graph G=(V,E) and a positive integer k and asks whether there exists a set E2 of at most k new edges so that the graph G2=(V,E∪E2) has diameter t. This problem is NP-hard (Schoone et al. 1987) [10], even in the t=2 case (Li et al. 1992) [7]. We give a parameterized reduction from Dominating Set to Diameter-tAugmentation to prove that Diameter-tAugmentation is W[2]-hard for every t.
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content type line 23
ISSN:0166-218X
1872-6771
DOI:10.1016/j.dam.2013.01.016