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Concurrent Iterated Local Search for the Maximum Weight Independent Set Problem

Authors Ernestine Großmann , Kenneth Langedal , Christian Schulz

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  • Theory of computation → Design and analysis of algorithms
Keywords
  • Randomized Local Search
  • Heuristics
  • Maximum Weight Independent Set
  • Algorithm Engineering
  • Parallel Computing

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Abstract

The Maximum Weight Independent Set problem is a fundamental NP-hard problem in combinatorial optimization with several real-world applications. Given an undirected vertex-weighted graph, the problem is to find a subset of the vertices with the highest possible weight under the constraint that no two vertices in the set can share an edge. This work presents a new iterated local search heuristic called CHILS (Concurrent Hybrid Iterated Local Search). The implementation of CHILS is specifically designed to handle large graphs of varying densities. CHILS outperforms the current state-of-the-art on commonly used benchmark instances, especially on the largest instances. As an added benefit, CHILS can run in parallel to leverage the power of multicore processors. The general technique used in CHILS is a new concurrent metaheuristic called Concurrent Difference-Core Heuristic that can also be applied to other combinatorial problems.

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Ernestine Großmann, Kenneth Langedal, and Christian Schulz. Concurrent Iterated Local Search for the Maximum Weight Independent Set Problem. In 23rd International Symposium on Experimental Algorithms (SEA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 338, pp. 22:1-22:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.SEA.2025.22

Author Details

Ernestine Großmann
  • Faculty of Mathematics and Computer Science, Heidelberg University, Germany
Kenneth Langedal
  • Department of Informatics, University of Bergen, Norway
Christian Schulz
  • Faculty of Mathematics and Computer Science, Heidelberg University, Germany

Funding

  • Großmann, Ernestine: Supported by DFG grant SCHU 2567/3-1.
  • Langedal, Kenneth: Supported by the Research Council of Norway under contract 303404 and Meltzer Research Fund, project number 104066111.

Acknowledgements

The inspiration for this work and collaboration started at the Dagstuhl Seminar 23491 on Scalable Graph Mining and Learning [Koutra et al., 2024]. We also thank Fredrik Manne for his helpful feedback throughout the writing process.

Supplementary Materials

References

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