Elsevier

Theoretical Computer Science

Volume 790, 22 October 2019, Pages 152-166
Theoretical Computer Science

Kernels for packing and covering problems

https://doi.org/10.1016/j.tcs.2019.04.018Get rights and content
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Abstract

We show how the notion of combinatorial duality, related to the well-known notion of duality from linear programming, may be used for translating kernel results obtained for packing problems into kernel results for covering problems. We exemplify this approach by having a closer look at the problems of packing a graph with vertex-disjoint trees or vertex-disjoint stars with r edges. The case r=2 has been studied in several other papers. By establishing a general notion of a crown, we show how linear-size vertex kernels can be efficiently achieved for the mentioned problems.

Keywords

Combinatorial problems
Packings
Coverings
Kernelization
Crown decomposition

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