The minimum coloring cut problem is defined as follows: given a connected graph G with colored edges, find an edge cut E' of G (a minimal set of edges whose removal renders the graph disconnected) such that the number of colors used by the edges in E' is minimum. In this work, we present two approaches based on variable neighborhood search to solve this problem. Our algorithms are able to find all the optimum solutions described in the literature.

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The bicluster editing problem (BEP) consists of editing (adding or removing) the edges of a bipartite graph G in order to transform it into a vertex‐disjoint union of complete bipartite subgraphs, in such a way that the sum of the weights of the edited edges is minimum. In this paper, we propose five parallel strategies for the implementation of a hybrid metaheuristic for the BEP, consisting of a GRASP with VNS as local search. Computational experiments show near‐linear speedups on Linux cluster with 64 processors and better solutions than those of the sequential approach.

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The NP-hard Bicluster Editing Problem (BEP) consists of editing a minimum number of edges of an input bipartite graph G in order to transform it into a vertex-disjoint union of complete bipartite subgraphs. Editing an edge consists of either adding it to the graph or deleting it from the graph. Applications of the BEP include data mining and analysis of gene expression data. In this work, we generate and analyze random bipartite instances for the BEP to perform empirical tests. A new reduction rule for the problem is proposed, based on the concept of critical independent sets, providing an effective reduction in the size of the instances. We also propose a set of heuristics using concepts of the metaheuristics ILS, VNS, and GRASP, including a constructive heuristic based on analyzing vertex neighborhoods, three local search procedures, and an auxiliary data structure to speed up the local search. Computational experiments show that our heuristics outperform other methods from the literature with respect to both solution quality and computational time.