On solving the densest k-subgraph problem on large graphs

Research output: Contribution to journalArticleScientificpeer-review


The densest k-subgraph problem is the problem of finding a k-vertex subgraph of a graph with the maximum number of edges. In order to solve large instances of the densest k-subgraph problem, we introduce two algorithms that are based on the random coordinate descent approach. Although it is common use to update at most two random coordinates simultaneously in each iteration of an algorithm, our algorithms may simultaneously update many coordinates. We show the benefit of updating more than two coordinates simultaneously for solving the densest k-subgraph problem, and solve large problem instances with up to 2^{15} vertices.
Original languageEnglish
Pages (from-to)1160-1178
JournalOptimization Methods and Software
Issue number6
Early online dateMar 2019
Publication statusPublished - Nov 2020


  • densest k-subgraph problem
  • random coordinate descent algorithm
  • large graphs


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