A divide-and-conquer approach for solving interval algebra networks

  • Authors:

  • Jason Jingshi Li;Jinbo Huang;Jochen Renz

  • Affiliations:

  • Australian National University, Canberra, ACT, Australia;National ICT Australia, Canberra, ACT, Australia;Australian National University, Canberra, ACT, Australia

  • Venue:
  • IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
  • Year:
  • 2009

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Abstract

Deciding consistency of constraint networks is a fundamental problem in qualitative spatial and temporal reasoning. In this paper we introduce a divide-and-conquer method that recursively partitions a given problem into smaller sub-problems in deciding consistency. We identify a key theoretical property of a qualitative calculus that ensures the soundness and completeness of this method, and show that it is satisfied by the Interval Algebra (IA) and the Point Algebra (PA). We develop a new encoding scheme for IA networks based on a combination of our divide-and-conquer method with an existing encoding of IA networks into SAT. We empirically show that our new encoding scheme scales to much larger problems and exhibits a consistent and significant improvement in efficiency over state-of-the-art solvers on the most difficult instances.