3 research outputs found
Relationship between clustering and algorithmic phase transitions in the random k-XORSAT model and its NP-complete extensions
We study the performances of stochastic heuristic search algorithms on
Uniquely Extendible Constraint Satisfaction Problems with random inputs. We
show that, for any heuristic preserving the Poissonian nature of the underlying
instance, the (heuristic-dependent) largest ratio of constraints per
variables for which a search algorithm is likely to find solutions is smaller
than the critical ratio above which solutions are clustered and
highly correlated. In addition we show that the clustering ratio can be reached
when the number k of variables per constraints goes to infinity by the
so-called Generalized Unit Clause heuristic.Comment: 15 pages, 4 figures, Proceedings of the International Workshop on
Statistical-Mechanical Informatics, September 16-19, 2007, Kyoto, Japan; some
imprecisions in the previous version have been correcte
The Satisfiability Threshold for a Seemingly Intractable Random Constraint Satisfaction Problem
We determine the exact threshold of satisfiability for random instances of a
particular NP-complete constraint satisfaction problem (CSP). This is the first
random CSP model for which we have determined a precise linear satisfiability
threshold, and for which random instances with density near that threshold
appear to be computationally difficult. More formally, it is the first random
CSP model for which the satisfiability threshold is known and which shares the
following characteristics with random k-SAT for k >= 3. The problem is
NP-complete, the satisfiability threshold occurs when there is a linear number
of clauses, and a uniformly random instance with a linear number of clauses
asymptotically almost surely has exponential resolution complexity.Comment: This is the long version of a paper that will be published in the
SIAM Journal on Discrete Mathematics. This long version includes an appendix
and a computer program. The contents of the paper are unchanged in the latest
version. The format of the arxiv submission was changed so that the computer
program will appear as an ancillary file. Some comments in the computer
program were update