Total domination and irredundance in weighted interval graphs

Total domination and irredundance in weighted interval graphs

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Article ID: iaor19881120
Country: United States
Volume: 1
Issue: 3
Start Page Number: 317
End Page Number: 327
Publication Date: Aug 1988
Journal: SIAM Journal On Discrete Mathematics
Authors: ,
Keywords: graphs, location
Abstract:

In an undirected graph, a subset X of the nodes is a total dominating set if each node in the graph is neighbour of some node in X. In contrast, X is an irredundant set if the closed neighbourhood of each node in X is not contained in the union of closed neighborhoods of the other nodes in X. This paper gives O(nlogn) and O(n4) time algorithms for finding, respectively, a minimum weighted total dominating set and a minimum weighted maximal irredundant set in a weighted interval graph, i.e., one that represents n intersecting intervals on the real line, each having a (possibly negative) real weight.

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