Faster parameterized algorithms for Bicluster Editing and Flip Consensus Tree

In the Bicluster Editing (resp., Flip Consensus Tree) problem the input is a bipartite graph G=(V1,V2,E) and an integer k, and the goal is to decide whether there is a set F⊆V1×V2 such that the graph (V1,V2,E△F) does not contain an induced path on four vertices (resp., an induced path on five vertices whose endpoints are in V2). In this paper we give algorithms for Bicluster Editing and Flip Consensus Tree whose running times are O⁎(2.22k) and O(3.24k), respectively. This improves over the O⁎(2.636k)-time algorithm for Bicluster Editing of Tsur [IPL 2021] and the O⁎(3.68k)-time algorithm for Flip Consensus Tree of Komusiewicz and Uhlmann [Algorithmica 2014].