Coping with the NP-Hardness of the Graph Bandwidth Problem
SWAT '00 Proceedings of the 7th Scandinavian Workshop on Algorithm Theory
Exact algorithms for NP-hard problems: a survey
Combinatorial optimization - Eureka, you shrink!
Maximum Matchings via Gaussian Elimination
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Inclusion--Exclusion Algorithms for Counting Set Partitions
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Fourier meets möbius: fast subset convolution
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Efficiency in exponential time for domination-type problems
Discrete Applied Mathematics
Graph-Theoretic Concepts in Computer Science
A measure & conquer approach for the analysis of exact algorithms
Journal of the ACM (JACM)
Exponential-time approximation of weighted set cover
Information Processing Letters
Counting Subgraphs via Homomorphisms
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Exact and Approximate Bandwidth
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Planar Capacitated Dominating Set Is W[1]-Hard
Parameterized and Exact Computation
An Exponential Time 2-Approximation Algorithm for Bandwidth
Parameterized and Exact Computation
Capacitated domination and covering: a parameterized perspective
IWPEC'08 Proceedings of the 3rd international conference on Parameterized and exact computation
Approximating the bandwidth of caterpillars
APPROX'05/RANDOM'05 Proceedings of the 8th international workshop on Approximation, Randomization and Combinatorial Optimization Problems, and Proceedings of the 9th international conference on Randamization and Computation: algorithms and techniques
Solving capacitated dominating set by using covering by subsets and maximum matching
WG'10 Proceedings of the 36th international conference on Graph-theoretic concepts in computer science
Scheduling partially ordered jobs faster than 2n
ESA'11 Proceedings of the 19th European conference on Algorithms
Capacitated domination: constant factor approximations for planar graphs
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
Finding a maximum induced degenerate subgraph faster than 2n
IPEC'12 Proceedings of the 7th international conference on Parameterized and Exact Computation
Solving Capacitated Dominating Set by using covering by subsets and maximum matching
Discrete Applied Mathematics
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In this paper we consider the Capacitated Dominating Set problem — a generalisation of the Dominating Set problem where each vertex v is additionally equipped with a number c(v), which is the number of other vertices this vertex can dominate. We provide an algorithm that solves Capacitated Dominating Set exactly in O(1.89n) time and polynomial space. Despite the fact that the Capacitated Dominating Set problem is quite similar to the Dominating Set problem, we are not aware of any published algorithms solving this problem faster than the straightforward O*(2n) solution prior to this paper. This was stated as an open problem at Dagstuhl seminar 08431 in 2008 and IWPEC 2008. We also provide an exponential approximation scheme for Capacitated Dominating Set which is a trade-off between the time complexity and the approximation ratio of the algorithm.