R. E. Vald'ez-P'erez. The satisfiability of temporal constraint networks. In IJCAI'89, pages 1291--1296, Menlo Park, Calif, USA, 1989.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....[35] it is very unlikely that other polynomial time algorithms will be found that solve this problem in general. Subsequent research has concentrated on designing more efficient reasoning algorithms, on identifying tractable special cases, and on isolating sources of computational complexity [10, 13, 14, 15, 16, 17, 22, 23, 28, 29, 31, 32, 33, 34, 35, 36]. However, it is by no means clear whether the tractable cases that have been identified are maximal and whether the sources of computational complexity found are the only ones. We extend these previous results in three ways. Firstly, we present a new tractable subclass of Allen s interval ....

....the complexity reduces to checking whether all relations fall into the ORD Horn subclass or not. Secondly, provided that a restriction to the ORD Horn subclass is not possible in an application, our results may be employed in designing faster backtracking algorithms for the full algebra [31, 33]. Since our subclass contains significantly more relations than other tractable subclasses, the branching factor in a backtrack search can be considerably decreased if the ORD Horn subclass is used. Acknowledgements We would like to thank Henry Kautz, Peter Ladkin, Len Schubert, Ron Shamir, Bart ....

R. E. Vald'ez-P'erez. The satisfiability of temporal constraint networks. In AAAI-87 [1], pages 256--260.

....for which the path consistency algorithm will find the minimal network. Montanari [27] shows that the path consistency algorithm finds the minimal network for a restricted class of binary constraint relations. However, the relations of interest here do not all fall into this class. Vald es P erez [37] shows that the path consistency algorithm finds the minimal network for IA networks which use only the basic interval relations. In [38, 40] we show that the path consistency algorithm finds the sets of feasible relations for the subclass of PA networks that do not contain the 6= relation, and ....

....end occurs in the search, the algorithm backs up to the last variable instantiated. For general constraint networks, Gaschnig [15] proposes backjumping as an improvement where the idea is to try and back up further to the source of the problem. For finding a consistent scenario, Vald es P erez [37] gives a backtracking algorithm in the style of backjumping. Improving the algorithms. Here we show how the results for SA networks can be used to improve the performance of backtracking algorithms for finding a consistent scenario. We then design a backtracking algorithm modeled on that of ....

R. E. Vald'es-P'erez. The satisfiability of temporal constraint networks. In Proceedings of the Sixth National Conference on Artificial Intelligence, pages 256--260, Seattle, Wash., 1987.

.... minimal network corresponding to the network given) This comes as no surprise since Vilain and Kautz [VK86] have showed that computing the satisfiability of a network of interval relations is an NP complete problem (as is computing the corresponding minimal network) Subsequently, Vald ez P erez [VP87] VP86] presented a dependency directed backtracking algorithm for computing a solution of an interval network if one exists and reporting unsatisfiability otherwise. Allen also presented some ideas on using reference intervals for clustering together events which are closely related. In his ....

R.E. Vald'es-P'erez. The Satisfiability of Temporal Constraint Networks. In Proceedings of AAAI-87, pages 256--260, 1987.

.... complexity is NP complete [27] and only subsets of interval algebra such as limited or no complete instances of the model, can be managed with a polynomial cost O(n 3 ) or O(n 4 ) where n is the number of nodes in the temporal graph, depending on whether there are disjunctive constraints or not [25, 24, 13]. A time point algebra is based on relative temporal relations ( and , as inequalities) between two time points. Algorithms for determining closure and consistency in full point algebra have a polynomial cost [27] By employing special structures, with a special consideration of the ....

Valdés-Perez R.E. The satisfiability of temporal constraints networks. Procc. 6th Nat. Conf. on Art. Intelligence (AAAI) Seatle, Wash. pp.256-260 (1987)

....for reasoning in Allen s interval algebra than previously believed if we are mainly interested in satisfiability. Provided that a restriction to the subclass H is not possible in an application, our results may be employed in designing faster backtracking algorithms for the full algebra (Vald ez P erez 1987; van Beek 1990) Since our subclass contains significantly more relations than other tractable subclasses, the branching factor in a backtrack search can be considerably decreased if the ORD Horn subclass is used. Finally, we showed that it is impossible to improve on our results. Using a ....

Vald'ez-P'erez, R. E. 1987. The satisfiability of temporal constraint networks. In Proc. 6th AAAI, 256--260.

.... They show that for continous domain, this result can be generalized to ternary and n ary constraints using some other notion of consistency ( 3,2) relational consistency) The class of CRC constraint is also related to discrete temporal reasoning [ van Beek, 1992b ] Vald esPeres [ Vald es P erez, 1987 ] shows that path consistency algorithms find the minimal network for a subclass of Allen s interval algebra [ Allen, 1983 ] Such a result has also been proposed in the context of point algebra [ Vilain and Kautz, 1986; van Beek, 1989 ] Montanari [ Montanari, 1974 ] already shows that a ....

R.E. Vald`es-P'erez. The satisfiability of temporal constraint network. In AAAI-87, Seattle, pages 745--750, 1987.

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R. E. Vald'ez-P'erez. The satisfiability of temporal constraint networks. In IJCAI'89, pages 1291--1296, Menlo Park, Calif, USA, 1989.

No context found.

Vald'es-P'erez, R. 1987. The satisfiability of temporal constraint networks. In Proceedings AAAI'87, 256-- 260.

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