Computing the k densest subgraphs of a graph

Riccardo Dondi, Danny Hermelin

Research output: Contribution to journalArticlepeer-review

Abstract

Computing cohesive subgraphs is a central problem in graph theory. While many formulations of cohesive subgraphs lead to NP-hard problems, finding a densest subgraph can be done in polynomial-time. As such, the densest subgraph model has emerged as the most popular notion of cohesiveness. Recently, the data mining community has started looking into the problem of computing k densest subgraphs in a given graph, rather than one. In this paper we consider a natural variant of the k densest subgraphs problem, where overlap between solution subgraphs is allowed with no constraint. We show that the problem is fixed-parameter tractable with respect to k, and admits a PTAS for constant k. Both these algorithms complement nicely the previously known O(nk) algorithm for the problem.

Original languageEnglish
Article number106316
Number of pages7
JournalInformation Processing Letters
Volume179
DOIs
StatePublished - Jan 2023

Keywords

  • Algorithm design
  • Algorithmic aspects of networks
  • Algorithms
  • Densest subgraph
  • Network mining and analysis

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Signal Processing
  • Information Systems
  • Computer Science Applications

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