Satisfiability of Quantitative Temporal Constraints with Multiple Granularities

Most work on temporal constraints has ignored the subtleties involved in dealing with multiple time granularities. This paper considers a constraint satisfaction problem (CSP) where binary quantitative constraints in terms of different time granularities can be specified on a set of variables, and unary constraints are allowed to limit the domain of variables. Such a CSP cannot be trivially reduced to one of the known CSP problems. The main result of the paper is a complete algorithm for checking consistency and finding a solution. The complexity of the algorithm is studied in the paper under different assumptions about the granularities involved in the CSP, and a second algorithm is proposed to improve the efficiency of the backtracking process needed to obtain all the solutions of the CSP. The work of Wang and Jajodia was partially supported by the National Science Foundation under the grant IRI-9633541.

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