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We study the performances of stochastic heuristic search algorithms onUniquely Extendible Constraint Satisfaction Problems with random inputs. Weshow that, for any heuristic preserving the Poissonian nature of the underlyinginstance, the (heuristic-dependent) largest ratio $\alpha_a$ of constraints pervariables for which a search algorithm is likely to find solutions is smallerthan the critical ratio $\alpha_d$ above which solutions are clustered andhighly correlated. In addition we show that the clustering ratio can be reachedwhen the number k of variables per constraints goes to infinity by theso-called Generalized Unit Clause heuristic.

Relationship between clustering and algorithmic phase transitions in the random k-XORSAT model and its NP-complete extensions