Twenty-One Large Tractable Subclasses of Allen's Algebra

Abstract This paper continues Nebel and Burckert's investigation of Allen's interval algebra by presenting nine more maximal tractable subclasses of the algebra (provided that P ≠ NP), in addition to their previously reported ORD-Horn subclass. Furthermore, twelve tractable subclasses are identified, whose maximality is not decided. Four of them can express the notion of sequentiality between intervals, which is not possible in the ORD-Horn algebra. All of the algebras are considerably larger than the ORD-Horn subclass. The satisfiability algorithm, which is common for all the algebras, is shown to be linear. Furthermore, the path consistency algorithm is shown to decide satisfiability of interval networks using any of the algebras.

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