Title of article :
SAT Distributions with Phase Transitions between Decision and Optimization Problems
Author/Authors :
Dimitriou، نويسنده , , Tassos، نويسنده ,
Issue Information :
روزنامه با شماره پیاپی سال 2003
Pages :
14
From page :
1
To page :
14
Abstract :
We present a generator for weighted instances of MAX k-SAT in which every clause has a weight associated with it and the goal is to maximize the total weight of satisfied clauses. Our generator produces formulas whose hardness can be finely tuned by two parameters p and δ that control the weights of the clauses. Under the right choice of these parameters an easy-hard-easy pattern in the search complexity emerges which is similar to the patterns observed for traditional SAT distributions. s remarkable, however, is that the generated distributions seem to lie in the middle ground between decision and optimization problems. Increasing the value of p from 0 to 1 has the effect of changing the shape of the computational cost from an easy-hard-easy pattern which is typical of decision problems to an easy-hard pattern which is typical of optimization problems. Thus our distributions seem to bridge the gap between decision and optimization versions of SAT. rmore, we demonstrate that these phase transitions are related to sudden changes to a quantity similar to the backbone of a SAT formula. In our model not only we know how the optimal solution looks like but we also prove it is unique. Thus our generator comes with a proof of the optimality of the best assignment which is basically the structural property that is related to the phase transition phenomena observed.
Journal title :
Electronic Notes in Discrete Mathematics
Serial Year :
2003
Journal title :
Electronic Notes in Discrete Mathematics
Record number :
1453635
Link To Document :
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