## Backdoors to typical case complexity (2003)

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Citations: | 87 - 12 self |

### BibTeX

@INPROCEEDINGS{Williams03backdoorsto,

author = {Ryan Williams and Carla P. Gomes},

title = {Backdoors to typical case complexity},

booktitle = {},

year = {2003},

pages = {1173--1178}

}

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### Abstract

There has been significant recent progress in reasoning and constraint processing methods. In areas such as planning and finite model-checking, current solution techniques can handle combinatorial problems with up to a million variables and five million constraints. The good scaling behavior of these methods appears to defy what one would expect based on a worst-case complexity analysis. In order to bridge this gap between theory and practice, we propose a new framework for studying the complexity of these techniques on practical problem instances. In particular, our approach incorporates general structural properties observed in practical problem instances into the formal complexity

### Citations

3994 |
Artificial Intelligence: a modern approach. Prentice-Hall, 2nd edition
- Russell, Norvig
- 2003
(Show Context)
Citation Context ...id-nineties, we saw the emergence of a more practical approach to computationally hard problems in AI, with the introduction of fast satisfiability solvers and fast constraint based reasoning methods =-=[17]-=-. For example, in planning we saw the success of constraint-based planners, such as Graphplan [2] and SatPlan 113], and most recently, heuristic search *Supported in part by an NSF Graduate Fellowship... |

989 | Fast Planning Through Planning Graph Analysis
- Blum, Furst
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(Show Context)
Citation Context ... AI, with the introduction of fast satisfiability solvers and fast constraint based reasoning methods [17]. For example, in planning we saw the success of constraint-based planners, such as Graphplan =-=[2]-=- and SatPlan 113], and most recently, heuristic search *Supported in part by an NSF Graduate Fellowship and the NSF ALADDIN Center. Research supported by AFOSR, Darpa, and the NSF. Bart Selman Dept. o... |

446 | Planning as satisfiability
- Kautz, Selman
- 1992
(Show Context)
Citation Context ...troduction of fast satisfiability solvers and fast constraint based reasoning methods [17]. For example, in planning we saw the success of constraint-based planners, such as Graphplan [2] and SatPlan =-=[13]-=-, and most recently, heuristic search based planners, e.g., [11; 8; 1]. Somewhat surprisingly, on practical problem instances these methods scale well beyond what one might expect based on a formal co... |

293 | Complexity and expressive power of logic programming - Dantsin, Eiter, et al. - 2001 |

280 | Using temporal logics to express search control knowledge for planning
- Bacchus, Kabanza
- 2000
(Show Context)
Citation Context ...ship and the NSF ALADDIN Center. Research supported by AFOSR, Darpa, and the NSF. Bart Selman Dept. of Computer Science Cornell University Ithaca, NY 14853 selman@cs.Cornell.edu based planners, e.g., =-=[11; 8; 1]-=-. Somewhat surprisingly, on practical problem instances these methods scale well beyond what one might expect based on a formal complexity analysis. In fact, current state-of-the-art SAT solvers can h... |

177 |
Determining computational complexity from characteristics “phrase transitions.” Nature
- Monasson, Zecchina, et al.
- 1999
(Show Context)
Citation Context ...h values of some of the variables. Our goal is to capture structural properties of real world problem instances. We start by reviewing the concept of a backbone in a SAT/CSP problem, as introduced in =-=[14]-=-. A variable is called a backbone variable if in all solutions to the CSP the variable is assigned the same value. Such variables are also called frozen variables [6]. Backbone variables are useful in... |

150 | Heavy-tailed Phenomena in Satisfiability and Constraint Satisfaction Problems
- Gomes, Selman, et al.
- 2000
(Show Context)
Citation Context ...erministic one with high probability (1 − 1/n, where n is the number of variables). This reflects the performance gain found in practice when backtracking SAT solvers are augmented with randomization =-=[15; 9]-=-. The third strategy yields tighter runtime bounds than the first two, but requires us to assume the existence of a good heuristic for choosing backdoor variables (which we find to be the case in prac... |

125 | Min and Anbulagan. Heuristics based on unit propagation and satisfiability problems
- Li
- 1997
(Show Context)
Citation Context ...on of the size of the backdoor. 3 Size of backdoors We did an empirical study of the size of backdoors in several practical SAT instances, using the SAT solver Satz-rand, a randomized version of Satz =-=[16]-=-. Satz incorporates powerful variable selection heuristics and an efficient simplification strategy (i.e., a good sub-solver). We modified Satz-rand to trace the variables selected for branching, and ... |

43 |
Smoothed analysis: Why the simplex algorithm usually takes polynomial time
- Spielman, Teng
(Show Context)
Citation Context ...ications. Theoretical computer scientists have been wellaware of the limitations of worst-case complexity results and have explored alternatives, such as average-case complexity and smoothed analysis =-=[20]-=-. In average-case analysis, one studies the computational cost of solving problem instances drawn from a predefined problem distribution. Such an analysis can provide valuable insights, as demonstrate... |

27 | Formal models of heavy-tailed behavior in combinatorial search - Chen, Gomes, et al. - 2001 |

25 |
Search Algorithms for Satisfiability Problems in Combinational Switching Circuits
- Silva
- 1995
(Show Context)
Citation Context ...pendent variables in a SAT encoding of a hardware verification problem is a backdoor for unit propagation, as the other variables' values may be directly determined after setting the independent ones =-=[19]-=-. There are two key questions concerning backdoors: What is the size of the backdoor in practical problem instances? When taking into account the cost of searching for a backdoor set, can one still ob... |

16 | I.: Well out of reach: why hard problems are hard
- Culberson, Gent
- 1999
(Show Context)
Citation Context ...AT/CSP problem, as introduced in [14]. A variable is called a backbone variable if in all solutions to the CSP the variable is assigned the same value. Such variables are also called frozen variables =-=[6]-=-. Backbone variables are useful in studying the properties of the solution space of a constraint satisfaction problem. Definition 2.1 [backbone] S is a backbone if there is a unique partial assignment... |

8 |
I.: Planning as propositional CSP: from Walksat to local search techniques for action graphs
- Gerevini, Serina
- 2003
(Show Context)
Citation Context ...electing a particular operator. A plan search technique that branches purely on the independent variables can obtain substantial speedups over search methods that do not exploit variable dependencies =-=[4]-=-. Another powerful intuition in the design of search methods is that one wants to select variables that simplify the problem instance as much as possible when these variables are assigned values. This... |

8 |
Exploiting variable dependency
- Kautz, McAllester, et al.
- 1997
(Show Context)
Citation Context ...is relatively small, one obtains a large improvement over searching the full space of variable/value assignments. We observe that independent variables are a particular kind of backdoor. As stated in =-=[12]-=-, they are a set S of variables for which all other variables may be thought of as defined in terms of S. For example, a maximal subset of independent variables in a SAT encoding of a hardware verific... |

8 |
Min and Anbulagan
- Li
- 1997
(Show Context)
Citation Context ... of the size of the backdoor. 3 Size of backdoors We did an empirical study of the size of backdoors in several practical SAT instances. We used the SAT solver Satz-rand, a randomized version of Satz =-=[16]-=-. Satz incorporates powerful variable selection heuristics and an efficient simplification strategy (i.e., a good sub-solver). Satz-rand was modified to trace the variable selection process and to kee... |

3 | 2001, ‘Formal Models of Heavy-tailed Behavior - Chen, Gomes, et al. |

1 |
benchmark cite
- SAT
(Show Context)
Citation Context ...s. These general insights have been incorporated in state-ofthe-art SAT and constraint solvers, and their effectiveness has been demonstrated empirically on a significant number of benchmark problems =-=[18]-=-. However, a more formal underpinning explaining the practical success of these strategies has been lacking. In this paper, we introduce a formal framework directly inspired by these techniques and pr... |