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An exact algorithm to find a maximum weight clique in a weighted undirected graph.

Kati Rozman1, An Ghysels2, Dušanka Janežič3

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We developed MaxCliqueWeight, a faster algorithm for finding maximum weight cliques in weighted graphs. This new method significantly improves computational speed on complex graph types, aiding research like drug discovery.

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Area of Science:

  • Graph Theory
  • Computational Complexity
  • Bioinformatics

Background:

  • The maximum weight clique problem is crucial in various fields, including computational biology and network analysis.
  • Existing algorithms struggle with computational efficiency on large and dense graphs.

Purpose of the Study:

  • Introduce MaxCliqueWeight, a novel algorithm for the maximum weight clique problem.
  • Enhance computational speed and efficiency for identifying cliques in weighted graphs.
  • Provide a freely available tool for the research community.

Main Methods:

  • Developed an efficient branch-and-bound approach.
  • Integrated a novel weighted graph coloring algorithm for determining upper weight bounds.
  • Evaluated performance on random and DIMACS benchmark graphs up to 10,000 nodes.

Main Results:

  • MaxCliqueWeight demonstrates significant improvements in computational speed compared to existing algorithms.
  • Outperforms alternatives by several orders of magnitude on high-density random and DIMACS graphs.
  • The algorithm's efficiency is particularly notable for large-scale graph analysis.

Conclusions:

  • MaxCliqueWeight offers a substantial advancement in solving the maximum weight clique problem.
  • The algorithm's speed and efficiency facilitate applications in areas like drug discovery.
  • The open availability of MaxCliqueWeight and its variant promotes wider research adoption and innovation.