NDLI: Approximation Algorithms and Hardness for Domination with Propagation

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Aazami, Ashkan Stilp, Kael
Copyright Year	2009
Abstract	The Power Dominating Set (PDS) problem is the following extension of the well-known dominating set problem: find a smallest-size set of nodes S that power dominates all the nodes, where a node v is power dominated if (1) v is in S or v has a neighbor in S, or (2) v has a neighbor w such that w and all of its neighbors except v are power dominated. We show a hardness of approximation threshold of $2^{\log^{1-\epsilon}n}$ in contrast to the logarithmic hardness for the dominating set problem. We give an $O(\sqrt{n})$-approximation algorithm for planar graphs and show that our methods cannot improve on this approximation guarantee. Finally, we initiate the study of PDS on directed graphs and show the same hardness threshold of $2^{\log^{1-\epsilon}n}$ for directed acyclic graphs. Also we show that the directed PDS problem can be solved optimally in linear time if the underlying undirected graph has bounded tree-width.
Starting Page	1382
Ending Page	1399
Page Count	18
File Format	PDF
ISSN	08954801
DOI	10.1137/06066672X
e-ISSN	10957146
Journal	SIAM Journal on Discrete Mathematics (SJDMEC)
Issue Number	3
Volume Number	23
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2009-09-23
Access Restriction	Subscribed
Subject Keyword	PMU placement problem tree-width greedy algorithms planar graphs hardness of approximation power dominating set Approximation algorithms approximation algorithms Combinatorial optimization dominating set
Content Type	Text
Resource Type	Article
Subject	Mathematics

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