A threshold of ln n for approximating set cover
Journal of the ACM (JACM)
Graph classes: a survey
Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties
Domination in Graphs Applied to Electric Power Networks
SIAM Journal on Discrete Mathematics
Treewidth: Algorithmoc Techniques and Results
MFCS '97 Proceedings of the 22nd International Symposium on Mathematical Foundations of Computer Science
Practical Algorithms on Partial k-Trees with an Application to Domination-like Problems
WADS '93 Proceedings of the Third Workshop on Algorithms and Data Structures
Bidimensionality: new connections between FPT algorithms and PTASs
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Approximation Algorithms and Hardness for Domination with Propagation
APPROX '07/RANDOM '07 Proceedings of the 10th International Workshop on Approximation and the 11th International Workshop on Randomization, and Combinatorial Optimization. Algorithms and Techniques
On the power domination number of the generalized Petersen graphs
Journal of Combinatorial Optimization
Generalized power domination of graphs
Discrete Applied Mathematics
Tree decompositions of graphs: Saving memory in dynamic programming
Discrete Optimization
A cutting-plane algorithm for solving a weighted influence interdiction problem
Computational Optimization and Applications
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The Power Dominating Set problem is a variant of the classical domination problem in graphs: Given an undirected graph G=(V,E), find a minimum P⊆V such that all vertices in V are “observed” by vertices in P. Herein, a vertex observes itself and all its neighbors, and if an observed vertex has all but one of its neighbors observed, then the remaining neighbor becomes observed as well. We show that Power Dominating Set can be solved by “bounded-treewidth dynamic programs.” Moreover, we simplify and extend several NP-completeness results, particularly showing that Power Dominating Set remains NP-complete for planar graphs, for circle graphs, and for split graphs. Specifically, our improved reductions imply that Power Dominating Set parameterized by |P| is W[2]-hard and cannot be better approximated than Dominating Set.