Trajectories in Phase Diagrams, Growth Processes, and Computational Complexity: How Search Algorithms Solve the 3-Satisfiability Problem

Simona Cocco; Rémi Monasson

doi:10.1103/PhysRevLett.86.1654

Trajectories in Phase Diagrams, Growth Processes, and Computational Complexity: How Search Algorithms Solve the 3-Satisfiability Problem

Simona Cocco and Rémi Monasson

Phys. Rev. Lett. 86, 1654 – Published 19 February 2001

Abstract

Decision and optimization problems typically fall into one of two categories for any particular solving algorithm. The problem is either solved quickly (easy) or demands an impractically long computational effort (hard). Here we show that some characteristic parameters of problems can be tracked during a run of the algorithm defining a trajectory through the parameter space. Focusing on 3-satisfiability, a recognized representative of hard problems, we analyze trajectories generated by search algorithms. These trajectories can cross well-defined phases, corresponding to domains of easy or hard instances, and allow one to successfully predict the times of resolution.

Received 15 September 2000

DOI:https://doi.org/10.1103/PhysRevLett.86.1654

Authors & Affiliations

Simona Cocco^* and Rémi Monasson^†

CNRS-Laboratoire de Physique Théorique de l'ENS, 24 rue Lhomond, 75005 Paris, France

^*Current address: Department of Physics, The University of Chicago, 845 W. Taylor Street, Chicago, IL 60607.
^†Current address: The James Franck Institute, The University of Chicago, 5640 S. Ellis Avenue, Chicago, IL 60637.