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Even Better Fixed-Parameter Algorithms for Bicluster Editing

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Computing and Combinatorics (COCOON 2020)

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Abstract

Given a bipartite graph G, the BICLUSTER EDITING problem asks for the minimum number of edges to insert or delete in G so that every connected component is a bicluster, i.e. a complete bipartite graph. This has applications in various areas such as social network analysis and bioinformatics. We study the parameterized complexity of the problem, the best published algorithm so far attaining a time of \(O^*(3.24^k)\), with k the number of edges to edit. Using novel but intuitive ideas, we significantly improve this to an \(O^*(2.695^k)\) time complexity.

Our algorithm has the advantage of being conceptually simple and does not require tedious case handling. Previous approaches were based on finding a forbidden induced subgraph (e.g. a \(P_4\)) and branching into several ways of eliminating such a subgraph. We take a departure from this local viewpoint, and instead solve conflicts globally. That is, we take two vertices that prevent the graph from containing only biclusters, and branch into the ways of resolving all the conflicts they are part of, at once. We hope that these ideas will allow simpler algorithms for other forbidden induced subgraph problems.

As a complementary result, we also show that BICLUSTER EDITING admits a problem kernel with 5k vertices.

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Notes

  1. 1.

    Notice that this could be divided into three cases: two of xy are with u, only one of them is, or none. However, our division into five cases makes the recursion calls to make more explicit.

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Correspondence to Manuel Lafond .

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Lafond, M. (2020). Even Better Fixed-Parameter Algorithms for Bicluster Editing. In: Kim, D., Uma, R., Cai, Z., Lee, D. (eds) Computing and Combinatorics. COCOON 2020. Lecture Notes in Computer Science(), vol 12273. Springer, Cham. https://doi.org/10.1007/978-3-030-58150-3_47

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  • DOI: https://doi.org/10.1007/978-3-030-58150-3_47

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