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In this paper we study the (in)approximability of two distance-based relaxed variants of the maximum clique problem (Max Clique), named Max d-Clique and Max d-Club: A d-clique in a graph $$G = (V, E)$$G=(V,E) is a subset $$S\subseteq V$$S⊆V of vertices ...

A d-clique in a graph $$G = V, E$$G=V,E is a subset $$S\subseteq V$$S⊆V of vertices such that for pairs of vertices $$u, v\in S$$u,v∈S, the distance between u and v is at most d in G. A d-club in a graph $$G = V, E$$G=V,E is a subset $$S'\subseteq V$$S'⊆...

We consider the combinatorial optimization problem where the objective function is the ratio of two linear functions. This type of problems can be solved by an algorithm that uses an auxiliary problem with a parametrized linear objective function. We ...