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SSS Algorithms for Max-Cut

Author

Listed:
  • Claudio Gentile

    (Istituto di Analisi dei Sistemi ed Informatica “A. Ruberti”, Consiglio Nazionale delle Ricerche, 00185 Rome, Italy)

  • Giovanni Rinaldi

    (Istituto di Analisi dei Sistemi ed Informatica “A. Ruberti”, Consiglio Nazionale delle Ricerche, 00185 Rome, Italy)

  • Esteban Salgado

    (Department of Industrial Engineering, Universidad Técnica Federico Santa María, Santiago 8940897, Chile)

Abstract

The subgraph sampling scheme (SSS) is a technique originally introduced for Markov random fields. It is a powerful tool for designing heuristic algorithms for max-cut, quadratic unconstrained binary optimization (QUBO), and other optimization problems. The first application of SSS in combinatorial optimization, combined with dynamic programming, is in Selby’s heuristic. This algorithm is shown to outperform quantum annealing for solving max-cut problems on chimera graphs. Leveraging SSS, we introduce two new algorithms. One is designed to handle general graphs, whereas the other is specifically tailored for toroidal grid graphs. To assess the effectiveness of these algorithms, we conducted a comprehensive evaluation. We used the same methodology, test bed, and set of 37 well-established heuristics for max-cut and QUBO problems as described in a recent study of Dunning, Gupta, and Silberholz. Notably, all three SSS-based algorithms consistently achieve top rankings in terms of performance.

Suggested Citation

  • Claudio Gentile & Giovanni Rinaldi & Esteban Salgado, 2026. "SSS Algorithms for Max-Cut," INFORMS Journal on Computing, INFORMS, vol. 38(3), pages 878-904, May.
    • Handle: RePEc:inm:orijoc:v:38:y:2026:i:3:p:878-904
    DOI: 10.1287/ijoc.2024.0812
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