20 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
Propagation connectivity of random hypergraphs
We study the concept of propagation connectivity on random 3-uniform hypergraphs. This concept is defined for investigating the performance of a simple algorithm for solving instances of certain constraint satisfaction problems. We derive upper and lower bounds for edge probability of random 3-uniform hypergraphs such that the propagation connectivity holds. Based on our analysis, we also show the way to implement the simple algorithm so that it runs in linear time on average