On selecting a satisfying truth assignment (extended abstract)
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
On the greedy algorithm for satisfiability
Information Processing Letters
Noise strategies for improving local search
AAAI '94 Proceedings of the twelfth national conference on Artificial intelligence (vol. 1)
The hardest constraint problems: a double phase transition
Artificial Intelligence
Empirical methods for artificial intelligence
Empirical methods for artificial intelligence
Experimental results on the crossover point in random 3-SAT
Artificial Intelligence - Special volume on frontiers in problem solving: phase transitions and complexity
The constrainedness knife-edge
AAAI '98/IAAI '98 Proceedings of the fifteenth national/tenth conference on Artificial intelligence/Innovative applications of artificial intelligence
On the run-time behaviour of stochastic local search algorithms for SAT
AAAI '99/IAAI '99 Proceedings of the sixteenth national conference on Artificial intelligence and the eleventh Innovative applications of artificial intelligence conference innovative applications of artificial intelligence
2+p-SAT: relation of typical-case complexity to the nature of the phase transition
Random Structures & Algorithms - Special issue on statistical physics methods in discrete probability, combinatorics, and theoretical computer science
SAT-Encodings, Search Space Structure, and Local Search Performance
IJCAI '99 Proceedings of the Sixteenth International Joint Conference on Artificial Intelligence
The complexity of theorem-proving procedures
STOC '71 Proceedings of the third annual ACM symposium on Theory of computing
EVIDENCE FOR A SATISFIABILITY THRESHOLD FOR RANDOM 3CNF FORMULAS
EVIDENCE FOR A SATISFIABILITY THRESHOLD FOR RANDOM 3CNF FORMULAS
When gravity fails: local search topology
Journal of Artificial Intelligence Research
Evidence for invariants in local search
AAAI'97/IAAI'97 Proceedings of the fourteenth national conference on artificial intelligence and ninth conference on Innovative applications of artificial intelligence
Clustering at the phase transition
AAAI'97/IAAI'97 Proceedings of the fourteenth national conference on artificial intelligence and ninth conference on Innovative applications of artificial intelligence
AAAI'96 Proceedings of the thirteenth national conference on Artificial intelligence - Volume 1
Tuning local search for satisfiability testing
AAAI'96 Proceedings of the thirteenth national conference on Artificial intelligence - Volume 1
Evolutionary algorithms for the satisfiability problem
Evolutionary Computation
Problem difficulty for tabu search in job-shop scheduling
Artificial Intelligence
Phase Transitions and Backbones of 3-SAT and Maximum 3-SAT
CP '01 Proceedings of the 7th International Conference on Principles and Practice of Constraint Programming
The Effects of Partial Restarts in Evolutionary Search
Selected Papers from the 5th European Conference on Artificial Evolution
SAT, Local Search Dynamics and Density of States
Selected Papers from the 5th European Conference on Artificial Evolution
On market-inspired approaches to propositional satisfiability
Artificial Intelligence
A mixture-model for the behaviour of SLS algorithms for SAT
Eighteenth national conference on Artificial intelligence
Lean clause-sets: generalizations of minimally unsatisfiable clause-sets
Discrete Applied Mathematics - The renesse issue on satisfiability
SAT problems with chains of dependent variables
Discrete Applied Mathematics - The renesse issue on satisfiability
Recognizing frozen variables in constraint satisfaction problems
Theoretical Computer Science
Evolving combinatorial problem instances that are difficult to solve
Evolutionary Computation
Stochastic local search for incremental SAT
International Journal of Knowledge-based and Intelligent Engineering Systems
Visualizing SAT Instances and Runs of the DPLL Algorithm
Journal of Automated Reasoning
Just enough learning (of association rules): the TAR2 "Treatment" learner
Artificial Intelligence Review
Computational complexity of auditing finite attributes in statistical databases
Journal of Computer and System Sciences
Probabilistically Estimating Backbones and Variable Bias: Experimental Overview
CP '08 Proceedings of the 14th international conference on Principles and Practice of Constraint Programming
A polynomial time computation of the exact correlation structure of k-satisfiability landscapes
Proceedings of the 11th Annual conference on Genetic and evolutionary computation
The backdoor key: a path to understanding problem hardness
AAAI'04 Proceedings of the 19th national conference on Artifical intelligence
Generating "random" 3-SAT instances with specific solution space structure
AAAI'04 Proceedings of the 19th national conference on Artifical intelligence
Journal of Artificial Intelligence Research
Understanding algorithm performance on an oversubscribed scheduling application
Journal of Artificial Intelligence Research
Backbones in optimization and approximation
IJCAI'01 Proceedings of the 17th international joint conference on Artificial intelligence - Volume 1
Understanding the behavior of Solution-Guided Search for job-shop scheduling
Journal of Scheduling
A backbone-based co-evolutionary heuristic for partial MAX-SAT
EA'05 Proceedings of the 7th international conference on Artificial Evolution
DPvis: a tool to visualize the structure of SAT instances
SAT'05 Proceedings of the 8th international conference on Theory and Applications of Satisfiability Testing
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The local search algorithm WSAT is one of the most successful algorithms for solving the satisfiability (SAT) problem. It is notably effective at solving hard Random 3-SAT instances near the so-called 'satisfiability threshold', but still shows a peak in search cost near the threshold and large variations in cost over different instances. We make a number of significant contributions to the analysis of WSAT on high-cost random instances, using the recently-introduced concept of the backbone of a SAT instance. The backbone is the set of literals which are entailed by an instance. We find that the number of solutions predicts the cost well for small-backbone instances but is much less relevant for the large-backbone instances which appear near the threshold and dominate in the overconstrained region. We show a very strong correlation between search cost and the Hamming distance to the nearest solution early in WSAT's search. This pattern leads us to introduce a measure of the backbone fragility of an instance, which indicates how persistent the backbone is as clauses are removed. We propose that high-cost random instances for local search are those with very large backbones which are also backbone-fragile. We suggest that the decay in cost beyond the satisfiability threshold is due to increasing backbone robustness (the opposite of backbone fragility). Our hypothesis makes three correct predictions. First, that the backbone robustness of an instance is negatively correlated with the local search cost when other factors are controlled for. Second, that backbone-minimal instances (which are 3-SAT instances altered so as to be more backbone-fragile) are unusually hard for WSAT. Third, that the clauses most often unsatisfied during search are those whose deletion has the most effect on the backbone. In understanding the pathologies of local search methods, we hope to contribute to the development of new and better techniques.