A complete classification of complexity in Allen's algebra in the presence of a non-trivial basic relation

  • Authors:

  • Andrei Krokhin;Peter Jeavons;Peter Jonsson

  • Affiliations:

  • Oxford University Computing Laboratory, Oxford, UK;Oxford University Computing Laboratory, Oxford, UK;Department of Computer and Information Science, Linköping University, Linköping, Sweden

  • Venue:
  • IJCAI'01 Proceedings of the 17th international joint conference on Artificial intelligence - Volume 1
  • Year:
  • 2001

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Abstract

We study fragments of Allen's algebra that contain a basic relation distinct from the equality relation. We prove that such a fragment is either NP-complete or else contained in some already known tractable subalgebra. We obtain this result by giving a new uniform description of known maximal tractable subalgebras and then systematically using an algebraic technique for description of maximal subalgebras with a given property. This approach avoids the need for extensive computerassisted search.