Approximation algorithms for NP-complete problems on planar graphs
Journal of the ACM (JACM)
A threshold of ln n for approximating set cover
Journal of the ACM (JACM)
Journal of the ACM (JACM)
Domination in Graphs Applied to Electric Power Networks
SIAM Journal on Discrete Mathematics
Approximation algorithms for combinatorial problems
STOC '73 Proceedings of the fifth annual ACM symposium on Theory of computing
Polynomial-time data reduction for dominating set
Journal of the ACM (JACM)
Subexponential parameterized algorithms on bounded-genus graphs and H-minor-free graphs
Journal of the ACM (JACM)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Dominating Sets in Planar Graphs: Branch-Width and Exponential Speed-Up
SIAM Journal on Computing
Capacitated domination and covering: a parameterized perspective
IWPEC'08 Proceedings of the 3rd international conference on Parameterized and exact computation
Capacitated Domination Problem
Algorithmica
Power domination problem in graphs
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
Linear problem kernels for NP-hard problems on planar graphs
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
Combinatorial Optimization on Graphs of Bounded Treewidth
The Computer Journal
Capacitated domination: constant factor approximations for planar graphs
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
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We consider the Capacitated Domination problem, which models a service-requirement assignment scenario and is a generalization to the well-known Dominating Set problem. In this problem, given a graph with three parameters defined on each vertex, namely cost, capacity, and demand, we want to find an assignment of demands to vertices of least cost such that the demand of each vertex is satisfied subject to the capacity constraint of each vertex providing the service. In terms of polynomial time approximations, we present logarithmic approximation algorithms with respect to different demand assignment models on general graphs. On the other hand, from the perspective of parameterization, we prove that this problem is W[1]-hard when parameterized by a structure of the graph called treewidth. Based on this hardness result, we present exact fixed-parameter tractable algorithms with respect to treewidth and maximum capacity of the vertices. This algorithm is further extended to obtain pseudo-polynomial time approximation schemes for planar graphs.