Journal of Computational Physics
Noise strategies for improving local search
AAAI '94 Proceedings of the twelfth national conference on Artificial intelligence (vol. 1)
Generating Satisfiable Problem Instances
Proceedings of the Seventeenth National Conference on Artificial Intelligence and Twelfth Conference on Innovative Applications of Artificial Intelligence
Balance and filtering in structured satisfiable problems
IJCAI'01 Proceedings of the 17th international joint conference on Artificial intelligence - Volume 1
From High Girth Graphs to Hard Instances
CP '08 Proceedings of the 14th international conference on Principles and Practice of Constraint Programming
Empirical hardness models: Methodology and a case study on combinatorial auctions
Journal of the ACM (JACM)
Further investigations into regular XORSAT
AAAI'06 proceedings of the 21st national conference on Artificial intelligence - Volume 2
A simple model to generate hard satisfiable instances
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
sgen1: A generator of small but difficult satisfiability benchmarks
Journal of Experimental Algorithmics (JEA)
Threshold behaviour of WalkSAT and focused metropolis search on random 3-satisfiability
SAT'05 Proceedings of the 8th international conference on Theory and Applications of Satisfiability Testing
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We introduce a highly structured family of hard satisfiable 3-SAT formulas corresponding to an ordered spin-glass model from statistical physics. This model has provably “glassy” behavior; that is, it has many local optima with large energy barriers between them, so that local search algorithms get stuck and have difficulty finding the true “ground state,” i.e., the unique satisfying assignment. We test the hardness of our formulas with two Davis-Putnam solvers, Satz and zChaff, the recently introduced Survey Propagation (SP), and two local search algorithms, WalkSAT and Record-to-Record Travel (RRT). We compare our formulas to random 3-XOR-SAT formulas and to two other generators of hard satisfiable instances, the minimum disagreement parity formulas of Crawford et al., and Hirsch’s hgen2. For the complete solvers the running time of our formulas grows exponentially in ${\sqrt n}$, and exceeds that of random 3-XOR-SAT formulas for small problem sizes. SP is unable to solve our formulas with as few as 25 variables. For WalkSAT, our formulas appear to be harder than any other known generator of satisfiable instances. Finally, our formulas can be solved efficiently by RRT but only if the parameter d is tuned to the height of the barriers between local minima, and we use this parameter to measure the barrier heights in random 3-XOR-SAT formulas as well.