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 several applications, including in bioinformatics and social network analysis. In this work, we study the parameterized complexity under the natural parameter k, which is the number of allowed modified edges. We first show that one can obtain a kernel with 4.5k vertices, an improvement over the previously known quadratic kernel. We then propose an algorithm that runs in time \(O^*(2.581^k)\). Our algorithm has the advantage of being conceptually simple and should be easy to implement.

给定一个二分图 G，双簇编辑问题要求在 G 中插入或删除的边数最少，以便每个连通分量都是一个双簇，即完整的二分图。这有多种应用，包括生物信息学和社交网络分析。在这项工作中，我们研究了自然参数 k 下的参数化复杂度，即允许修改的边的数量。我们首先证明可以获得具有 4.5k 个顶点的内核，这是对先前已知的二次内核的改进。然后，我们提出了一种在时间 \(O^*(2.581^k)\) 中运行的算法。我们的算法的优点是概念简单并且易于实现。