Linear Kernel for Planar Connected Dominating Set
TAMC '09 Proceedings of the 6th Annual Conference on Theory and Applications of Models of Computation
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
A linear kernel for a planar connected dominating set
Theoretical Computer Science
Kernel bounds for disjoint cycles and disjoint paths
Theoretical Computer Science
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We consider the following problem: given a planar graph G = (V,E) and integer k, find if possible at least k vertex disjoint cycles in G. This problem is known to be NP-complete. In this paper, we give a number of simple data reduction rules. Each rule transforms the input to an equivalent smaller input, and can be carried out in polynomial time. We show that inputs on which no rule can be carried out have size linear in k. Thereby we obtain that the k -Disjoint Cycles problem on planar graphs has a kernel of linear size. We also present a parameterized algorithm with a running time of $O(c^{\sqrt{k}} + n^2)$.