An Exact Exponential Time Algorithm for Power Dominating Set

The Power Dominating Set problem is an extension of the well-known domination problem on graphs in a way that we enrich it by a second propagation rule: given a graph G ( V , E ), a set P ⊆ V is a power dominating set if every vertex is observed after the exhaustive application of the following two...

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Bibliographic Details
Published in:Algorithmica Vol. 63; no. 1-2; pp. 323 - 346
Main Authors: Binkele-Raible, Daniel, Fernau, Henning
Format: Journal Article
Language:English
Published: New York Springer-Verlag 01.06.2012
Springer
Subjects:
Algorithm Analysis and Problem Complexity
Algorithmics. Computability. Computer arithmetics
Algorithms
Applied sciences
Computer Science
Computer science; control theory; systems
Computer Systems Organization and Communication Networks
Data Structures and Information Theory
Exact sciences and technology
Mathematics of Computing
Theoretical computing
Theory of Computation
Measure and conquer
Domination-type problems
Moderately exponential time algorithms
hardness results
Dominating set
Cubic graph
Algorithmics
Pointer
Graph theory
NP-hardness results
NP hard problem
Problem solving
Subgraph
Search tree
Non local theory
ISSN:0178-4617, 1432-0541
Online Access:Get full text
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Summary:The Power Dominating Set problem is an extension of the well-known domination problem on graphs in a way that we enrich it by a second propagation rule: given a graph G ( V , E ), a set P ⊆ V is a power dominating set if every vertex is observed after the exhaustive application of the following two rules. First, a vertex is observed if v ∈ P or it has a neighbor in P . Secondly, if an observed vertex has exactly one unobserved neighbor u , then also u will be observed, as well. We show that Power Dominating Set remains -hard on cubic graphs. We design an algorithm solving this problem in time on general graphs, using polynomial space only. To achieve this, we introduce so-called reference search trees that can be seen as a compact representation of usual search trees, providing non-local pointers in order to indicate pruned subtrees.
ISSN:0178-4617
1432-0541
DOI:10.1007/s00453-011-9533-2