Parameterized reductions and algorithms for a graph editing problem that generalizes vertex cover
Artikel i vetenskaplig tidskrift, 2012

We study a novel generalization of the Vertex Cover problem which is motivated by, e.g., error correction (data cleaning) prior to 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 its 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 exactly 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 exactly the union of some stars, i.e., vertices with all their incident edges. Our time bound is O*(1.84^c) where c denotes the total number of recolored edges.

vertex cover

graph editing

parameterized complexity

error correction

hitting set

problem kernel


Peter Damaschke

Chalmers, Data- och informationsteknik, Datavetenskap

Leonid Molokov

Chalmers, Data- och informationsteknik, Datavetenskap

Theoretical Computer Science

0304-3975 (ISSN)

Vol. 452 39-46


Grundläggande vetenskaper


Bioinformatik (beräkningsbiologi)

Datavetenskap (datalogi)

Diskret matematik



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