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## P 3 C: A New Algorithm for the Simple Temporal Problem

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Citations: | 17 - 3 self |

### Citations

1298 |
Introduction to Graph Theory
- West
- 1996
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Citation Context ...on, we list some definitions and theorems from graph theory which underlie the new algorithm we propose in the next section. These results are readily available in graph-theoretical literature, e.g. (=-=West 1996-=-). Definition 3. Let G = 〈V, E〉 be an undirected graph. We can define the following concepts: • A vertex v ∈ V is simplicial if the set of its neighbours Nv = {w | {v, w} ∈ E} induces a clique, i.e. i... |

1128 | Temporal constraint networks
- Dechter, Meiri, et al.
- 1991
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Citation Context ...ty EEMCS, Delft University of Technology, The Netherlands b Cork Constraint Computation Centre, University College Cork, Ireland The Simple Temporal Problem (STP) was first proposed by Dechter et al. =-=[1]-=-. An STP instance consists of a set of time-point variables and a set of constraints that bound the time difference between pairs of these variables. The goal is then to find out all possible time val... |

686 | Constraint Processing - Dechter - 2003 |

649 | Automated Planning: Theory and Practice - Ghallab, Nau, et al. - 2004 |

484 |
Networks of constraints: Fundamental properties and applications to picture processing
- Montanari
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Citation Context ... Floyd-Warshall is simple to implement and runs in O � n 3� time, where n is the number of time-point variables in the STP instance. It corresponds to enforcing the property of path consistency (PC) (=-=Montanari 1974-=-), known from constraint satisfaction theory. For checking whether an STP instance is consistent, Dechter et al. proposed directed path consistency (DPC), which we include as Algorithm 1. The algorith... |

116 | Backtracking algorithms for disjunctions of temporal constraints
- Stergiou, Koubarakis
- 2000
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Citation Context ...in more expressive formalisms for temporal reasoning, such as the Temporal Constraint Satisfaction Problem—proposed by Dechter et al. in conjunction with the STP—and the Disjunctive Temporal Problem (=-=Stergiou and Koubarakis 2000-=-). For our purposes, we will focus on the importance of the STP for temporal planning (Nau, Ghallab, and Traverso 2004, Chapter 15). Traditionally, planning has been concerned with finding out which a... |

41 | Planning the Project Management Way: Efficient Planning by Effective Integration of Causal and Resource Reasoning in RealPlan - Srivastava, Kambhampati, et al. |

39 | Triagulation of Graphs - Algorithms Giving Small Total State Space
- Kjærulff
- 1990
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Citation Context ...mum if there exists no triangulation T ′ with |T ′ | < |T |. Determining a minimum triangulation is an NP-complete problem; in contrast, a (locally) minimal triangulation can be found in O (nm) time (=-=Kjærulff 1990-=-). Since finding the smallest triangulations is so hard, several heuristics have been proposed for this problem. Kjærulff has found that both the minimum fill and minimum degree heuristics produce goo... |

36 | A new efficient algorithm for solving the Simple Temporal Problem
- Xu, Choueiry
- 2003
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Citation Context ...rested in calculating an equivalent decomposable STP instance, from which all solutions can then be extracted in a backtrack-free manner. The fastest known algorithm to attain decomposability is △STP =-=[3]-=-, included as Algorithm 1. Instead of considering a complete constraint graph, as its predecessors do, this algorithm works on a chordal constraint graph, which generally contains far less edges. A gr... |

20 | The SMT-LIB Format: An Initial Proposal
- Ranise, Tinelli
- 2003
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Citation Context ...uadratic, and our new P 3 C algorithm remains linear in the amount of triangles, as was proven above. The instances of the job-shop problem we considered are taken from the SMT-LIB benchmark library (=-=Ranise and Tinelli 2003-=-). In effect, these are instances of the NP-hard Disjunctive Temporal Problem (DTP): each constraint is a disjunction of temporal inequalities. We generated a set of STP instances by randomly selectin... |

18 | Path Consistency for Triangulated Constraint Graphs - Bliek, Sam-Haroud - 1999 |

16 | Integrating Planning and Scheduling
- Garrido, Barber
- 2001
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Citation Context ...e parts are treated as separate problems. Whereas Crikey tries to decouple planning and scheduling as much as possible, other people have taken an iterative approach. Both (Myers and Smith 1999) and (=-=Garrido and Barber 2001-=-) discuss this type of approach in general. 1 Application of the architecture sketched here is not limited to scheduling over time; Srivastava, Kambhampati, and Do (2001) propose a similar architectur... |

15 | Development of Iterative Real-Time Scheduler to Planner Feedback - McVey, Atkins, et al. - 1997 |

12 | ASPEN: A framework for automated planning and scheduling of spacecraft control and operations
- Fukunaga, Rabideau, et al.
- 1997
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Citation Context ...tion does not exist. The STP has received widespread attention that still lasts today, with applications in such areas as medical informatics (Anselma et al. 2006), spacecraft control and operations (=-=Fukunaga et al. 1997-=-), and air traffic control (Buzing and Witteveen 2004). Moreover, the STP appears as a pivotal subproblem in more expressive formalisms for temporal reasoning, such as the Temporal Constraint Satisfac... |

10 | Issues in the Integration of Planning and Scheduling for Enterprise Control
- Myers, Smith
- 1999
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Citation Context ...lved together; the separable parts are treated as separate problems. Whereas Crikey tries to decouple planning and scheduling as much as possible, other people have taken an iterative approach. Both (=-=Myers and Smith 1999-=-) and (Garrido and Barber 2001) discuss this type of approach in general. 1 Application of the architecture sketched here is not limited to scheduling over time; Srivastava, Kambhampati, and Do (2001)... |

9 | A Temporal Constraint Network Based Temporal Planner - Castillo, Fernández-Olivares, et al. - 2002 |

7 | Planning with timed literals and deadlines - Cresswell, Coddington |

4 | Distributed (re) planning with preference information
- Buzing, Witteveen
- 2004
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Citation Context ...read attention that still lasts today, with applications in such areas as medical informatics (Anselma et al. 2006), spacecraft control and operations (Fukunaga et al. 1997), and air traffic control (=-=Buzing and Witteveen 2004-=-). Moreover, the STP appears as a pivotal subproblem in more expressive formalisms for temporal reasoning, such as the Temporal Constraint Satisfaction Problem—proposed by Dechter et al. in conjunctio... |

4 | CRIKEY- a temporal planner looking at the integration of Planning and Scheduling - Halsey, Long, et al. |

3 | Dynamic sequencing of tasks in simple temporal networks with uncertainty - Vidal, Bidot |