Solving qualitative constraints involving landmarks

Authors:
Weiming Liu;Shengsheng Wang;Sanjiang Li;Dayou Liu
Affiliations:
Centre for Quantum Computation and Intelligent Systems, Faculty of Engineering and Information Technology, University of Technology Sydney, Australia;College of Computer Science and Technology, Jilin University, Changchun, China;Centre for Quantum Computation and Intelligent Systems, Faculty of Engineering and Information Technology, University of Technology Sydney, Australia;College of Computer Science and Technology, Jilin University, Changchun, China
Venue:
CP'11 Proceedings of the 17th international conference on Principles and practice of constraint programming
Year:
2011

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Abstract

Consistency checking plays a central role in qualitative spatial and temporal reasoning. Given a set of variables V, and a set of constraints Γ taken from a qualitative calculus (e.g. the Interval Algebra (IA) or RCC-8), the aim is to decide if Γ is consistent. The consistency problem has been investigated extensively in the literature. Practical applications e.g. urban planning often impose, in addition to those between undetermined entities (variables), constraints between determined entities (constants or landmarks) and variables. This paper introduces this as a new class of qualitative constraint satisfaction problems, and investigates the new consistency problem in several well-known qualitative calculi, e.g. IA, RCC-5, and RCC-8. We show that the usual local consistency checking algorithm works for IA but fails in RCC-5 and RCC-8. We further show that, if the landmarks are represented by polygons, then the new consistency problem of RCC-5 is tractable but that of RCC-8 is NP-complete.