STCSP - Structured temporal constraint satisfaction problems

Temporal Constraint Satisfaction Problems (TCSP) is a well-known 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 obtained; 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 sub-problems that share at most pairs of time points. Such decompositions are termed sim/2-tree decompositions. For TCSPs that have sim/2-tree decompositions, minimal constraints of input propositions can be computed by independent computations of the minimal networks of the sub-problems at most twice. It is also shown that the sim/2-tree characterization is a minimal set of conditions. The sim/2-tree decomposition extends former results about decomposition of a TCSP into bi-connected components. An algorithm for identifying a sim/2-tree decomposition of a TCSP is provided as well. Finally, the sim/2-tree 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 ≤ n), where STCSP⁽⁰⁾ is simply TCSP, STCSP⁽¹⁾ is a set of STCSP⁽⁰⁾s, and in general, STCSP⁽ⁿ⁾ for 1 ≤ n is a set of STCSP^(n-1)s, is introduced.