Solving Connected Dominating Set Faster than 2 n
Algorithmica - Parameterized and Exact Algorithms
Planar Capacitated Dominating Set Is W[1]-Hard
Parameterized and Exact Computation
Partitioning into Sets of Bounded Cardinality
Parameterized and Exact Computation
Capacitated domination and covering: a parameterized perspective
IWPEC'08 Proceedings of the 3rd international conference on Parameterized and exact computation
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
Solving connected dominating set faster than 2n
FSTTCS'06 Proceedings of the 26th international conference on Foundations of Software Technology and Theoretical Computer Science
Capacitated domination faster than O(2n)
SWAT'10 Proceedings of the 12th Scandinavian conference on Algorithm Theory
Exact (exponential) algorithms for the dominating set problem
WG'04 Proceedings of the 30th international conference on Graph-Theoretic Concepts in Computer Science
A faster algorithm for dominating set analyzed by the potential method
IPEC'11 Proceedings of the 6th international conference on Parameterized and Exact Computation
Parameterized Complexity
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The Capacitated Dominating Set problem is the problem of finding a dominating set of minimum cardinality where each vertex has been assigned a bound on the number of vertices it has capacity to dominate. Cygan et al. showed in 2009 that this problem can be solved in O(n^3mnn/3) or in O^*(1.89^n) time using maximum matching algorithm. An alternative way to solve this problem is to use dynamic programming over subsets. By exploiting structural properties of instances that cannot be solved fast by the maximum matching approach, and ''hiding'' additional cost related to considering subsets of large cardinality in the dynamic programming, an improved algorithm is obtained. We show that the Capacitated Dominating Set problem can be solved in O^*(1.8463^n) time.