Expected gains from parallelizing constraint solving for hard problems
AAAI '94 Proceedings of the twelfth national conference on Artificial intelligence (vol. 1)
Easy problems are sometimes hard
Artificial Intelligence
Solving Real-World Linear Programs: A Decade and More of Progress
Operations Research
Heuristics based on unit propagation for satisfiability problems
IJCAI'97 Proceedings of the 15th international joint conference on Artifical intelligence - Volume 1
Sparse constraint graphs and exceptionally hard problems
IJCAI'95 Proceedings of the 14th international joint conference on Artificial intelligence - Volume 1
Backdoors to typical case complexity
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
Tradeoffs in the complexity of backdoor detection
CP'07 Proceedings of the 13th international conference on Principles and practice of constraint programming
Operations Research Letters
Backdoors in the Context of Learning
SAT '09 Proceedings of the 12th International Conference on Theory and Applications of Satisfiability Testing
IPCO'11 Proceedings of the 15th international conference on Integer programming and combinatoral optimization
INFORMS Journal on Computing
Crowdsourcing backdoor identification for combinatorial optimization
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
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There has been considerable interest in the identification of structural properties of combinatorial problems that lead, directly or indirectly, to the development of efficient algorithms for solving them. One such concept is that of a backdoor set--a set of variables such that once they are instantiated, the remaining problem simplifies to a tractable form. While backdoor sets were originally defined to capture structure in decision problems with discrete variables, here we introduce a notion of backdoors that captures structure in optimization problems, which often have both discrete and continuous variables. We show that finding a feasible solution and proving optimality are characterized by backdoors of different kinds and size. Surprisingly, in certain mixed integer programming problems, proving optimality involves a smaller backdoor set than finding the optimal solution. We also show extensive results on the number of backdoors of various sizes in optimization problems. Overall, this work demonstrates that backdoors, appropriately generalized, are also effective in capturing problem structure in optimization problems.