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- W2129188082 abstract "In this paper we introduce a natural generalization of the well-known problems Cluster Editing and Bicluster Editing, whose parameterized versions have been intensively investigated in the recent literature. The generalized problem, called Mixed Cluster Editing or ${cal M}$-Cluster Editing, is formulated as follows. Let ${cal M}$ be a family of graphs. Given a graph $G$ and a nonnegative integer $k$, transform $G$, through a sequence of at most $k$ edge editions, into a target graph $G'$ with the following property: $G'$ is a vertex-disjoint union of graphs $G_1, G_2, ldots$ such that every $G_i$ is a member of ${cal M}$. The graph $G'$ is called a mixed cluster graph or ${cal M}$-cluster graph. Let ${cal K}$ denote the family of complete graphs, ${cal KL}$ the family of complete $l$-partite graphs ($l geq 2$), and $Ł={cal K} cup {cal KL}$. In this work we focus on the case ${cal M} = {cal L}$. Using modular decomposition techniques previously applied to Cluster/Bicluster Editing, we present a linear-time algorithm to construct a problem kernel for the parameterized version of ${cal L}$-Cluster Editing. Keywords: bicluster graphs, cluster graphs, edge edition problems, edge modification problems, fixed-parameter tractability, NP-complete problems." @default.
- W2129188082 created "2016-06-24" @default.
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- W2129188082 date "2015-06-02" @default.
- W2129188082 modified "2023-09-27" @default.
- W2129188082 title "Parameterized mixed cluster editing via modular decomposition" @default.
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