Algorithms for 2-club cluster deletion problems using automated generation of branching rules

Abstract

In the 2-Club Cluster Vertex Deletion (resp., 2-Club Cluster Edge Deletion) problem the input is a graph G and an integer k, and the goal is to decide whether there is a set of at most k vertices (resp., edges) whose removal from G results in a graph in which the diameter of every connected component is at most 2. In this paper we give algorithms for 2-Club Cluster Vertex Deletion and 2-Club Cluster Edge Deletion whose running times are O⁎(3.104k) and O⁎(2.562k), respectively. Our algorithms were obtained using automated generation of branching rules. Our results improve the previous O⁎(3.303k)-time algorithm for 2-Club Cluster Vertex Deletion [Liu et al., FAW-AAIM 2012] and the O⁎(2.695k)-time algorithm for 2-Club Cluster Edge Deletion [Abu-Khzam et al., TCS 2023].