Abstract
AbstractFinding densest subgraphs is a fundamental problem in graph mining, with several applications in different fields. In this paper, we consider two variants of the problem of covering a graph with k densest subgraphs, where \(k \ge 2\). The first variant aims to find a collection of k subgraphs of maximum density, the second variant asks for a set of k subgraphs such that they maximize an objective function that includes the sum of the subgraphs densities and a distance function, in order to differentiate the computed subgraphs. We show that the first variant of the problem is solvable in polynomial time, for any \(k \ge 2\). For the second variant, which is NP-hard for \(k \ge 3\), we present an approximation algorithm that achieves a factor of \(\frac{2}{5}\).
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