An Improved Fixed-Parameter Algorithm for 2-Club Cluster Edge Deletion
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A 2-club is a graph of diameter at most two. In the decision version of the parametrized 2-Club Cluster Edge Deletion problem, an undirected graph G is given along with an integer k≥ 0 as parameter, and the question is whether G can be transformed into a disjoint union of 2-clubs by deleting at most k edges. A simple fixed-parameter algorithm solves the problem in 𝒪^*(3^k), and a decade-old algorithm was claimed to have an improved running time of 𝒪^*(2.74^k) via a sophisticated case analysis. Unfortunately, this latter algorithm suffers from a flawed branching scenario. In this paper, an improved fixed-parameter algorithm is presented with a running time in 𝒪^*(2.695^k).
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