Improved Kernelization and Fixed-parameter Algorithms for Bicluster Editing

TL;DR

This paper improves the kernel size and proposes a simple fixed-parameter algorithm for the Bicluster Editing problem, making it more efficient and practical for applications in bioinformatics and social network analysis.

Contribution

It introduces a smaller kernel with 4.5k vertices and a straightforward algorithm with runtime O*(2.581^k) for Bicluster Editing, advancing parameterized complexity techniques.

Findings

Kernel size reduced to 4.5k vertices

Algorithm runs in O*(2.581^k) time

Algorithm is simple and easy to implement

Abstract

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.