Campus Units

Mathematics

Document Type

Article

Publication Version

Accepted Manuscript

Publication Date

4-2019

Journal or Book Title

Journal of Combinatorial Optimization

Volume

37

Issue

3

First Page

935

Last Page

956

DOI

10.1007/s10878-018-0330-6

Abstract

Power domination in graphs arises from the problem of monitoring an electric power system by placing as few measurement devices in the system as possible. A power dominating set of a graph is a set of vertices that observes every vertex in the graph, following a set of rules for power system monitoring. A practical problem of interest is to determine the minimum number of additional measurement devices needed to monitor a power network when the network is expanded and the existing devices remain in place. In this paper, we study the problem of finding the smallest power dominating set that contains a given set of vertices X. We also study the related problem of finding the smallest zero forcing set that contains a given set of vertices X. The sizes of such sets in a graph G are respectively called the restricted power domination number and restricted zero forcing number of G subject to X. We derive several tight bounds on the restricted power domination and zero forcing numbers of graphs, and relate them to other graph parameters. We also present exact and algorithmic results for computing the restricted power domination number, including integer programs for general graphs and a linear time algorithm for graphs with bounded treewidth. We also use restricted power domination to obtain a parallel algorithm for finding minimum power dominating sets in trees.

Comments

This is a post-peer-review, pre-copyedit version of an article published in Journal of Combinatorial Optimization. The final authenticated version is available online at DOI: 10.1007/s10878-018-0330-6. Posted with permission.

Copyright Owner

Springer Science+Business Media, LLC

Language

en

File Format

application/pdf

Published Version

Share

COinS