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The backtracking survey propagation algorithm for solving random K-SAT problems

Author

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  • Raffaele Marino

    (NORDITA and AlbaNova University Centre, KTH-Royal Institute of Technology and Stockholm University)

  • Giorgio Parisi

    (Sapienza Università di Roma and Istituto Nazionale di Fisica Nucleare, Sezione di Roma1 and CNR-Nanotec)

  • Federico Ricci-Tersenghi

    (Sapienza Università di Roma and Istituto Nazionale di Fisica Nucleare, Sezione di Roma1 and CNR-Nanotec)

Abstract

Discrete combinatorial optimization has a central role in many scientific disciplines, however, for hard problems we lack linear time algorithms that would allow us to solve very large instances. Moreover, it is still unclear what are the key features that make a discrete combinatorial optimization problem hard to solve. Here we study random K-satisfiability problems with K=3,4, which are known to be very hard close to the SAT-UNSAT threshold, where problems stop having solutions. We show that the backtracking survey propagation algorithm, in a time practically linear in the problem size, is able to find solutions very close to the threshold, in a region unreachable by any other algorithm. All solutions found have no frozen variables, thus supporting the conjecture that only unfrozen solutions can be found in linear time, and that a problem becomes impossible to solve in linear time when all solutions contain frozen variables.

Suggested Citation

  • Raffaele Marino & Giorgio Parisi & Federico Ricci-Tersenghi, 2016. "The backtracking survey propagation algorithm for solving random K-SAT problems," Nature Communications, Nature, vol. 7(1), pages 1-8, December.
    • Handle: RePEc:nat:natcom:v:7:y:2016:i:1:d:10.1038_ncomms12996
    DOI: 10.1038/ncomms12996
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    Cited by:

    1. Xu, Wei & Zhang, Zhe & Zhou, Guangyan, 2023. "Generating hard satisfiable instances by planting into random constraint satisfaction problem model with growing constraint scope length," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 609(C).

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