## Computational Aspects of Reordering Plans (1998)

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Venue: | Journal of Artificial Intelligence Research |

Citations: | 59 - 0 self |

### BibTeX

@ARTICLE{Bäckström98computationalaspects,

author = {Christer Bäckström},

title = {Computational Aspects of Reordering Plans},

journal = {Journal of Artificial Intelligence Research},

year = {1998},

volume = {9},

pages = {99--137}

}

### Years of Citing Articles

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### Abstract

This article studies the problem of modifying the action ordering of a plan in order to optimise the plan according to various criteria. One of these criteria is to make a plan less constrained and the other is to minimize its parallel execution time. Three candidate definitions are proposed for the first of these criteria, constituting a sequence of increasing optimality guarantees. Two of these are based on deordering plans, which means that ordering relations may only be removed, not added, while the third one uses reordering, where arbitrary modifications to the ordering are allowed. It is shown that only the weakest one of the three criteria is tractable to achieve, the other two being NP-hard and even difficult to approximate. Similarly, optimising the parallel execution time of a plan is studied both for deordering and reordering of plans. In the general case, both of these computations are NP-hard. However, it is shown that optimal deorderings can be computed in polynomial time...

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382 | On the hardness of approximating minimization problems - Lund, Yannakakis - 1994 |

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Citation Context ...ions. In some planning systems, eg O-Plan (Currie & Tate, 1991) and Sipe (Wilkins, 1988), both planning and scheduling are integrated into one single system. Similarly, temporal planners, eg Deviser (=-=Vere, 1983-=-) and IxTeT (Ghallab & Laruelle, 1994), can often reason also about metric constraints. This does not make it c fl1998 AI Access Foundation and Morgan Kaufmann Publishers. All rights reserved. B ackst... |

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Citation Context ...the scheduler to control the reordering process, or to try other reorderings. One could imagine a reordering algorithm which uses either heuristic search or randomized local-search methods a la GSAT (=-=Selman, Levesque, & Mitchell, 1992-=-) to nd reorderings and then use the scheduler as evaluation function for the proposed reorderings. While the plan modi cations studied in this article may add considerably to the optimizations that a... |

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Formulating multiagent dynamic-world problems in the classical planning framework
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Citation Context ...der polynomial time by topological sorting, it is less obvious that also the converse holds. At least three algorithms for converting t.o. plans into p.o. plans have been presented in the literature (=-=Pednault, 1986-=-; Regnier & Fade, 1991a; Veloso, P'erez, & Carbonell, 1990) (all these algorithms will be analyzed later in this article). The claim that a t.o. plan can easily be converted into a p.o. plan is vacuou... |

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Citation Context ...ied version of an existing assembly line for toy cars used for undergraduate laborations in digital control at Linkoping University (for a description of this assembly line, see eg. Klein, Jonsson, & =-=Backstrom, 1995-=-, 1998; Stromberg, 1991). The problem is to assemble a LEGO 2 car from pre-assembled parts as shown in Figure 1. There is a chassis, a top and a set of wheels, the two latter to be mounted onto the ch... |

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22 |
Interacting goals and their use
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Citation Context ...plan is least constrained and, to some extent, this also depends on the purpose of achieving least-constrainment. The major motivation for producing p.o. plans instead of t.o. plans (see for instance =-=Tate, 1975-=-) is that a p.o. plan can be post-processed by a scheduler according to further criteria, such as release times and deadlines or resource limits. Either the actions are ordered into an (ideally) optim... |

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Citation Context ... minimum-constrained reordering of P wrt. \Pi iff (a) Q is a reordering P wrt. \Pi and (b) there is no reordering hA; OE 00 iof Q wrt. \Pi s.t. j OE 00 j ! j OE j; Note that the previous publication (=-=Backstrom, 1993-=-) used the terms LC1-minimality for minimal-constrained deordering and LC2-minimality for minimum-constrained reordering. This change in terminology has been done with the hope that more will be gaine... |

17 | B.: Complete determination of parallel actions and temporal optimization in linear plans of action - Regnier, Fade - 1991 |

14 | Formalizing plan justifications - Fink, Yang - 1992 |

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10 |
A threshold of ln n for approximating set cover (preliminary version
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Citation Context ...nal atoms in the plan as a measure of its size, this bound can be strengthened to (1 \Gamma ") ln jPj for arbitrary " unless NP 2 DTIME (n log log n ) by substituting such a result for Minim=-=um Cover (Feige, 1996-=-) in the proof above. 5. Parallel Plans In order to study the problem of finding a shortest parallel execution of a plan, the formalisms used so far are not quite sufficient. Since they lack a capabil... |

10 | Tractable planning for an assembly line - Klein, Jonsson, et al. |

7 | Efficient planning for a miniature assembly line - Klein, Jonsson, et al. - 2000 |

5 | Executing parallel plans faster by adding actions
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Citation Context ...rn hA; OE + i; Figure 7: The minimal-deordering algorithm MLD In particular, note that plan validation is polynomial for the usual variant of propositional STRIPS without conditional actions (Nebel & =-=Backstrom, 1994-=-, Theorem 5.9). More precisely, this proof pertains to the Common Propositional STRIPS formalism (CPS) and, thus, holds also for the other common variants of propositional STRIPS, like Ground TWEAK (B... |

5 | Combining the Expressivity of UCPOP with the E ciency of Graphplan - Gazen, Knoblock - 1997 |

4 |
Styrning av LEGO-bilfabrik. andra omarbetade upplagan
- Stromberg
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Citation Context ...ing assembly line for toy cars used for undergraduate laborations in digital control at Linkoping University (for a description of this assembly line, see eg. Klein, Jonsson, & Backstrom, 1995, 1998; =-=Stromberg, 1991-=-). The problem is to assemble a LEGO 2 car from pre-assembled parts as shown in Figure 1. There is a chassis, a top and a set of wheels, the two latter to be mounted onto the chassis. Top Chassis Whee... |

2 | Formalizing plan justi cations - Fink, Yang - 1992 |

2 |
A uni ed framework for explanation-based generalization of partially ordered and partially instantiated plans
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Citation Context ...lso to make partially ordered plans more partially ordered, that is, to generalise the ordering. An algorithm for this task has been presented in the literature in the context of case-based planning (=-=Kambhampati & Kedar, 1994-=-). Since t.o. plan are just a special case of p.o. plans, this section will study the general problem of making partially ordered plans less constrained. 108s4.1 Least-constrainment Criteria Computati... |

1 | Computational Aspects of Reordering Plans - Regnier - 1991 |