An algorithm for linear programming which requires O(((m+n)n2+(m+n)1.5n)L) arithmetic operations
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
Combinatorial optimization: algorithms and complexity
Combinatorial optimization: algorithms and complexity
Introduction to algorithms
Artificial Intelligence - Special issue on knowledge representation
Reasoning about temporal relations: a maximal tractable subclass of Allen's interval algebra
Journal of the ACM (JACM)
A unifying approach to temporal constraint reasoning
Artificial Intelligence
Building tractable disjunctive constraints
Journal of the ACM (JACM)
Maintaining knowledge about temporal intervals
Communications of the ACM
Tractable disjunctions of linear constraints: basic results and applications to temporal reasoning
Theoretical Computer Science
A New Framework for Reasoning about Points, Intervals and Durations
IJCAI '99 Proceedings of the Sixteenth International Joint Conference on Artificial Intelligence
A New Tractable Subclass of the Rectangle Algebra
IJCAI '99 Proceedings of the Sixteenth International Joint Conference on Artificial Intelligence
On finding a solution in temporal constraint satisfaction problems
IJCAI'97 Proceedings of the Fifteenth international joint conference on Artifical intelligence - Volume 2
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Several methods for temporal reasoning with metric time have been suggested--for instance, Horn Disjunctive Linear Relations (Horn DLRs). However, it has been noted that implementing this algorithm is non-trivial since it builds on fairly complicated polynomial-time algorithms for linear Perogramming. Instead, an alternative approach which augments Allen's interval algebra with a Simple Temporal Problem (STP) has been suggested (Condotta, 2000). In this paper, we present a new point-based approach STP* for reasoning about metric temporal constraints. STP* subsumes the tractable preconvex fragment of the augmented interval algebra and can be viewed as a slightly restricted version of Horn DLRs. We give an easily implementable algorithm for deciding satisfiability of STP* and demonstrate experimentally its efficiency. We also give a method for finding solutions to consistent STP* problem instances.