A linear-time algorithm for broadcast domination in a tree

The broadcast domination problem is a variant of the classical minimum dominating set problem in which a transmitter of power p at vertex v is capable of dominating (broadcasting to) all vertices within distance p from v. Our goal is to assign a broadcast power f(v) to every vertex v in a graph such...

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Bibliographic Details
Published in:Networks Vol. 53; no. 2; pp. 160 - 169
Main Authors: Dabney, John, Dean, Brian C., Hedetniemi, Stephen T.
Format: Journal Article
Language:English
Published: Hoboken Wiley Subscription Services, Inc., A Wiley Company 01.03.2009
Subjects:
broadcasts
domination
linear-time algorithms
tree algorithms
ISSN:0028-3045, 1097-0037
Online Access:Get full text
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Summary:The broadcast domination problem is a variant of the classical minimum dominating set problem in which a transmitter of power p at vertex v is capable of dominating (broadcasting to) all vertices within distance p from v. Our goal is to assign a broadcast power f(v) to every vertex v in a graph such that ΣvεVf(v) is minimized, and such that every vertex u with f(u) = 0 is within distance f(v) of some vertex v with f(v)> 0. The problem is solvable in polynomial time on a general graph (Heggernes and Lokshtanov, Disc Math (2006), 3267–3280) and Blair et al. (Congr. Num. (2004), 55–77.) gave an O(n2) algorithm for trees. In this article, we provide an O(n) algorithm for trees. Our algorithm is notable due to the fact that it makes decisions for each vertex v based on “nonlocal” information from vertices far away from v, whereas almost all other linear‐time algorithms for trees only make use of local information. © 2008 Wiley Periodicals, Inc. NETWORKS, 2009
Bibliography:ArticleID:NET20275
istex:35306D19CF5224177278820F1D73AD028D7253E9
ark:/67375/WNG-0V6WHWL5-Z
ISSN:0028-3045
1097-0037
DOI:10.1002/net.20275