Treffer: A dynamic programming algorithm for the maximum [formula omitted]-club problem on trees.

Computing cliques in an undirected graph G = (V G , E G) is a fundamental problem in social network analysis. However, in some cases, the strict definition of a clique (a subset of vertices pairwise adjacent in G) often limits its applicability in real-world settings. To address this issue, we study the s -club: a clique relaxation that induces a subgraph of diameter at most s. Note that a clique is simply a 1-club. Computing a maximum s -club is a computationally challenging problem, as it is NP-hard for any positive integer s in arbitrary graphs. Thus, this paper presents a simple dynamic programming algorithm that efficiently computes a maximum s -club on an n -vertex tree in O (s ⋅ n) time. This algorithm outperforms existing algorithms for trees in theory and practice. This approach is a stepping stone towards computing maximum s -clubs on tree-like graphs. • A simple dynamic programming approach to compute a maximum s -club on trees. • For an arbitrary n -vertex tree, the presented algorithm runs in O (s ⋅ n) time. • Experimental results (on real and synthetic trees) confirm the theoretical analysis. [ABSTRACT FROM AUTHOR]

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