Circumspect descent prevails in solving random constraint satisfaction problems. We study the performance of stochastic local search algorithms for random instances of the K-satisfiability (K-SAT) problem. We present a stochastic local search algorithm, ChainSAT, which moves in the energy landscape of a problem instance by never going upwards in energy. ChainSAT is a focused algorithm in the sense that it focuses on variables occurring in unsatisfied clauses. We show by extensive numerical investigations that ChainSAT and other focused algorithms solve large K-SAT instances almost surely in linear time, up to high clause-to-variable ratios α; for example, for K = 4 we observe linear-time performance well beyond the recently postulated clustering and condensation transitions in the solution space. The performance of ChainSAT is a surprise given that by design the algorithm gets trapped into the first local energy minimum it encounters, yet no such minima are encountered. We also study the geometry of the solution space as accessed by stochastic local search algorithms.

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  1. Budzynski, Louise; Semerjian, Guilhem: Biased measures for random constraint satisfaction problems: larger interaction range and asymptotic expansion (2020)
  2. Achlioptas, Dimitris; Iliopoulos, Fotis; Kolmogorov, Vladimir: A local lemma for focused stochastic algorithms (2019)
  3. Budzynski, Louise; Ricci-Tersenghi, Federico; Semerjian, Guilhem: Biased landscapes for random constraint satisfaction problems (2019)
  4. Braunstein, Alfredo; Dall’Asta, Luca; Semerjian, Guilhem; Zdeborová, Lenka: The large deviations of the whitening process in random constraint satisfaction problems (2016)
  5. Caniou, Yves; Codognet, Philippe; Richoux, Florian; Diaz, Daniel; Abreu, Salvador: Large-scale parallelism for constraint-based local search: the costas array case study (2015)
  6. Angione, Claudio; Occhipinti, Annalisa; Nicosia, Giuseppe: Satisfiability by Maxwell-Boltzmann and Bose-Einstein statistical distributions (2014)
  7. Angione, Claudio; Occhipinti, Annalisa; Stracquadanio, Giovanni; Nicosia, Giuseppe: Bose-Einstein condensation in satisfiability problems (2013)
  8. Ahmed, Furqan; Tirkkonen, Olav; Peltomäki, Matti; Koljonen, Juha-Matti; Yu, Chia-Hao; Alava, Mikko: Distributed graph coloring for self-organization in LTE networks (2010) ioport
  9. Albrecht, A. A.; Lane, P. C. R.; Steinhöfel, K.: Analysis of local search landscapes for (k)-SAT instances (2010)
  10. Alava, Mikko; Ardelius, John; Aurell, Erik; Kaski, Petteri; Krishnamurthy, Supriya; Orponen, Pekka; Seitz, Sakari: Circumspect descent prevails in solving random constraint satisfaction problems (2007) ioport