Complexity and algorithms for constant diameter augmentation problems

•For given integers d, k and graph G, can we obtain a graph with diameter d via at most k edge deletions?•We determine the computational complexity of this and related problems for different values of d.•For d=3, the problem is related to Moore graphs and solvable in polynomial time.•For all d>4,...

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Bibliographic Details
Published in:Theoretical computer science Vol. 904; pp. 15 - 26
Main Authors: Kim, Eun Jung, Milanič, Martin, Monnot, Jérôme, Picouleau, Christophe
Format: Journal Article
Language:English
Published: Elsevier B.V 15.02.2022
Subjects:
Blocker problem
Graph diameter
NP-complete
Polynomial algorithm
Graph diameter
Blocker problem
NP-complete
Polynomial algorithm
ISSN:0304-3975, 1879-2294
Online Access:Get full text
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Summary:•For given integers d, k and graph G, can we obtain a graph with diameter d via at most k edge deletions?•We determine the computational complexity of this and related problems for different values of d.•For d=3, the problem is related to Moore graphs and solvable in polynomial time.•For all d>4, the problem is NP-complete.•The NP-completeness results are proved for various values of the diameter of the input graph. We study the following problem: for given integers d,k and graph G, can we obtain a graph with diameter d via at most k edge deletions? We determine the computational complexity of this and related problems for different values of d.
ISSN:0304-3975
1879-2294
DOI:10.1016/j.tcs.2021.05.020