## Backtracking Algorithms for Disjunctions of Temporal Constraints (1998)

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Venue: | Artificial Intelligence |

Citations: | 111 - 2 self |

### BibTeX

@ARTICLE{Stergiou98backtrackingalgorithms,

author = {Kostas Stergiou and Manolis Koubarakis and Manchester M Qd},

title = {Backtracking Algorithms for Disjunctions of Temporal Constraints},

journal = {Artificial Intelligence},

year = {1998},

volume = {120},

pages = {248--253}

}

### Years of Citing Articles

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### Abstract

We extend the framework of simple temporal problems studied originally by Dechter, Meiri and Pearl to consider constraints of the form x1 \Gamma y1 r1 : : : xn \Gamma yn rn , where x1 : : : xn ; y1 : : : yn are variables ranging over the real numbers, r1 : : : rn are real constants, and n 1. We have implemented four progressively more efficient algorithms for the consistency checking problem for this class of temporal constraints. We have partially ordered those algorithms according to the number of visited search nodes and the number of performed consistency checks. Finally, we have carried out a series of experimental results on the location of the hard region. The results show that hard problems occur at a critical value of the ratio of disjunctions to variables. This value is between 6 and 7. Introduction Reasoning with temporal constraints has been a hot research topic for the last fifteen years. The importance of this problem has been demonstrated in many areas of artifici...

### Citations

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Citation Context ...e.g., planning, scheduling, spatio-temporal databases, geographical information systems and medical information systems. The class of quantitative temporal constraints has been studied originally by (=-=Dechter et al., 1989-=-) in the framework of simple temporal problems (STPs) where constraints are of the form x \Gamma ysc where x and y are real variables and c is a real constant, and temporal constraint satisfaction pro... |

864 | Foundations of Constraint Satisfaction - Tsang - 1993 |

698 | A New Method for Solving Hard Satisfiability Problems - Selman, Levesque, et al. - 1996 |

603 | Where the really hard problems are
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Citation Context ...ith respect to the number of search tree nodes visited, the number of consistency checks performed, and the CPU time used. Then, we tried to investigate the phase transition in the problem we study. (=-=Cheeseman et al., 1991-=-; Prosser, 1996; Smith and Dyer, 1996; Selman et al., 1996; Gent and Walsh, 1996; Crawford and Auton, 1996) showed that for many NP-complete problems, hard problems occur arround a critical value of a... |

421 | Minimizing Conflicts: A Heuristic Repair Method for Constraint-Satisfaction and Scheduling Problems - Minton, Johnston, et al. - 1992 |

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148 | Combining Qualitative and Quantitative Constraints in Temporal Reasoning - Meiri - 1991 |

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An Empirical Study of Phase Transitions in Binary Constraint Satisfaction Problems
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Citation Context ...r of search tree nodes visited, the number of consistency checks performed, and the CPU time used. Then, we tried to investigate the phase transition in the problem we study. (Cheeseman et al., 1991; =-=Prosser, 1996-=-; Smith and Dyer, 1996; Selman et al., 1996; Gent and Walsh, 1996; Crawford and Auton, 1996) showed that for many NP-complete problems, hard problems occur arround a critical value of a control parame... |

113 | Integrating Metric and Qualitative Temporal Reasoning - Kautz, Ladkin - 1991 |

100 | Generating hard satisfiability problems
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Citation Context ...umber of consistency checks performed, and the CPU time used. Then, we tried to investigate the phase transition in the problem we study. (Cheeseman et al., 1991; Prosser, 1996; Smith and Dyer, 1996; =-=Selman et al., 1996-=-; Gent and Walsh, 1996; Crawford and Auton, 1996) showed that for many NP-complete problems, hard problems occur arround a critical value of a control parameter. The control parameter in our problem i... |

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38 |
Experimental evaluation of preprocessing algorithms for constraint satisfaction problems
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Citation Context ...egy in CSPs is to preprocess the set of constraints prior to the search. Preprocessing tries to reduce the search space that backtracking algorithms explore, and in that way improve their efficiency (=-=Dechter and Meiri, 1994-=-). The set of disjunctions D can be reduced to an equivalent smaller subset by applying three simple pruning rules prior to the execution of the search algorithm: 1. If a disjunction D(i) contains a d... |

38 | Processing disjunctions in temporal constraint networks
- Schwalb, Dechter
- 1997
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Citation Context ...t, and temporal constraint satisfaction problems (TCSPs) where constraints are disjunctions of formulas lsx \Gamma ysu involving the same pair of real variables x and y (l and u are real constants). (=-=Schwalb and Dechter, 1997-=-) studied the performance of local consistency algorithms for processing TCSPs on hard problems in the transition region. This work was carried out in the context of project CHOROCHRONOS funded by the... |

35 | Efficient algorithms for qualitative reasoning about time
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Citation Context ... non-disjunctive constraints so that the new set of constraints produced is still consistent. The Algorithm First we introduce some necessary terminology. Some of it is similar to the terminology of (=-=Gerevini and Schubert, 1995-=-). The given set of disjunctions will be denoted by D. D(i) and D(i,j) will represent the i-th disjunction and the j-th disjunct of the i-th disjunction, respectively. The set of non-disjunctive const... |

35 | Generating Feasible Schedules under Complex Metric Constraints - Cheng, Smith - 1994 |

35 | Database Models for Infinite and Indefinite Temporal .Information - Koubarakis - 1994 |

33 | The satisfiability constraint gap
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Citation Context ...checks performed, and the CPU time used. Then, we tried to investigate the phase transition in the problem we study. (Cheeseman et al., 1991; Prosser, 1996; Smith and Dyer, 1996; Selman et al., 1996; =-=Gent and Walsh, 1996-=-; Crawford and Auton, 1996) showed that for many NP-complete problems, hard problems occur arround a critical value of a control parameter. The control parameter in our problem is the ratio r of disju... |

30 | Efficient Temporal Reasoning through Timegraphs - Gerevini, Schubert |

29 | Locating the Phase Transition in Constraint Satisfaction Problems
- Smith
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(Show Context)
Citation Context ...e nodes visited, the number of consistency checks performed, and the CPU time used. Then, we tried to investigate the phase transition in the problem we study. (Cheeseman et al., 1991; Prosser, 1996; =-=Smith and Dyer, 1996-=-; Selman et al., 1996; Gent and Walsh, 1996; Crawford and Auton, 1996) showed that for many NP-complete problems, hard problems occur arround a critical value of a control parameter. The control param... |

29 | In search of the best constraint satisfaction search - Frost, Dechter - 1994 |

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26 | A linear programming approach to temporal reasoning - Jonsson, Bäckström |

24 | Dense time and temporal constraints with 6 - Koubarakis - 1992 |

24 | The Complexity of Query Evaluation in Indefinite Temporal Constraint Databases - Koubarakis - 1997 |

23 | Twenty-one large tractable subclasses of Allen’s algebra - Drakengren, Jonsson - 1997 |

23 | Temporal query processing with indefinite information - Beek |

20 | Temporal reasoning in timegraph I-II - Gerevini, Schubert, et al. |

20 | Some pitfalls for experimenters with random SAT - Mitchell, Levesque - 1996 |

19 | Maximal Tractable Subclasses of Allen’s Interval Algebra: Preliminary Report - Drakengren, Jonsson - 1996 |

18 | Efcient algorithms for networks of quantitative temporal constraints
- Chleq
- 1995
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Citation Context ...nstraints can be decided in two steps. First, we check the consistency of the subset of non-disjunctive constraints. This is done using the incremental directional path consistency algorithm IDPC of (=-=Chleq, 1995-=-). If the subset of nondisjunctive constraints is consistent, we consider the subset of disjunctive constraints as well. Now C is consistent if for each disjunction there exists one disjunct that can ... |

17 | local to global consistency in temporal constraint networks,” Theoretical - Koubarakis, “From - 1997 |

11 | A symbolic approach to interval constraint problems - Ladkin, Reinefeld - 1993 |