STCSP – structured temporal constraint satisfaction problems

Abstract

Temporal Constraint Satisfaction Problems (TCSP) is a welldknown approach for representing and processing temporal knowledge. Important properties of the knowledge can be inferred by computing the minimal networks of TCSPs. Consistency and feasible values are immediately obtaineds computing solutions can be assisted. Yet, in general, computing the minimal network of a disjunctive TCSP is intractable. The minimal network approach requires computation of the full network in order to answer a query. In this paper we characterize TCSPs for which subsets of the minimal network can be computed without having to compute the whole network. The partial computation is enabled by decomposition of the problem into a tree of subdproblems that share at most pairs of time points. Such decompositions are termed sim/2dtree decompositions. For TCSPs that have sim/2dtree decompositions, minimal constraints of input propositions can be computed by independent computations of the minimal networks of the subdproblems at most twice. It is also shown that the sim/2dtree characterization is a minimal set of conditions. The sim/2dtree decomposition extends former results about decomposition of a TCSP into bidconnected components. An algorithm for identifying a sim/2dtree decomposition of a TCSP is provided as well. Finally, the sim/2dtree decomposition is generalized in an inductive manner, which enables components of a decomposition to be further decomposed. For that purpose a model of Structured Temporal Constraint Satisfaction Problems (STCSP^{(n)},\ 0 \leq n), where STCSP^{(0)} is simply TCSP, STCSP^{(1)} is a set of STCSP^{(0)}s, and in general, STCSP^{(n)} for 1 \leq n is a set of STCSP^{(n-1)}s, is introduced.