Note: The parametric complexity of graph diameter augmentation

Authors:
Yong Gao;Donovan R. Hare;James Nastos
Affiliations:
Department of Computer Science, University of British Columbia Okanagan, Kelowna, British Columbia, V1V 1V7, Canada;Department of Mathematics, University of British Columbia Okanagan, Kelowna, British Columbia, V1V 1V7, Canada;Department of Computer Science, University of British Columbia Okanagan, Kelowna, British Columbia, V1V 1V7, Canada
Venue:
Discrete Applied Mathematics
Year:
2013

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Abstract

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 E"2 of at most k new edges so that the graph G"2=(V,E@?E"2) 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.