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Covering a Graph with Densest Subgraphs

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Algorithms and Discrete Applied Mathematics (CALDAM 2022)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 13179))

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Abstract

Finding 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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Authors and Affiliations

  1. Università degli Studi di Bergamo, Bergamo, Italy

    Riccardo Dondi

  2. University of Bucharest, Bucharest, Romania

    Alexandru Popa

Authors
  1. Riccardo Dondi
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  2. Alexandru Popa
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Correspondence to Riccardo Dondi .

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Editors and Affiliations

  1. Indian Institute of Technology Bombay, Mumbai, India

    Niranjan Balachandran

  2. Indian Institute of Technology Guwahati, Guwahati, India

    R. Inkulu

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Dondi, R., Popa, A. (2022). Covering a Graph with Densest Subgraphs. In: Balachandran, N., Inkulu, R. (eds) Algorithms and Discrete Applied Mathematics. CALDAM 2022. Lecture Notes in Computer Science(), vol 13179. Springer, Cham. https://doi.org/10.1007/978-3-030-95018-7_13

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  • DOI: https://doi.org/10.1007/978-3-030-95018-7_13

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-95017-0

  • Online ISBN: 978-3-030-95018-7

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