Given a bipartite graph $G$, the \textsc{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.

翻译：给定一个二分图$G$，\textsc{Bicluster Editing}问题要求插入或删除最少数量的边，使得$G$的每个连通分量都成为一个双簇，即一个完全二分图。该问题在生物信息学和社会网络分析等领域具有多种应用。本文中，我们研究了该问题在自然参数$k$（即允许修改的边数）下的参数化复杂度。我们首先证明可以获得一个具有$4.5k$个顶点的核，这改进了先前已知的二次核。随后，我们提出了一种运行时间为$O^*(2.581^k)$的算法。我们的算法具有概念简单的优点，且易于实现。