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2011 | OriginalPaper | Chapter

Parameterized Reductions and Algorithms for Another Vertex Cover Generalization

Authors : Peter Damaschke, Leonid Molokov

Published in: Algorithms and Data Structures

Publisher: Springer Berlin Heidelberg

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We study a novel generalization of the

Vertex Cover

problem which is motivated by, e.g., error correction in the inference of chemical mixtures by their observable reaction products. We focus on the important case of deciding on one of two candidate substances. This problem has nice graph-theoretic formulations situated between

Vertex Cover

and

3-Hitting Set

. In order to characterize their parameterized complexity we devise parameter-preserving reductions, and we show that some minimum solution can be computed faster than by solving

3-Hitting Set

in general. More explicitly, we introduce the

Union Editing

problem: In a hypergraph with red and blue vertices, edit the colors so that the red set becomes the union of some hyperedges. The case of degree 2 is equivalent to

Star Editing

: In a graph with red and blue edges, edit the colors so that the red set becomes the union of some stars, i.e., vertices with

all

their incident edges.

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Metadata
Title
Parameterized Reductions and Algorithms for Another Vertex Cover Generalization
Authors
Peter Damaschke
Leonid Molokov
Copyright Year
2011
Publisher
Springer Berlin Heidelberg
DOI
https://doi.org/10.1007/978-3-642-22300-6_24

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