Constraint Networks of Topological Relations and Convexity

  • Authors:

  • Ernest Davis;Nicholas Mark Gotts;Anthony G. Cohn

  • Affiliations:

  • Dept. of Computer Science, New York University;Land Use Science Group, Macaulay Land Use Research Institute, Aberdeen, UK;School of Computer Studies, University of Leeds

  • Venue:
  • Constraints
  • Year:
  • 1999

Quantified Score

Hi-index 0.00

Visualization

Abstract

Thispaper studies the expressivity and computational complexity ofnetworks of constraints of topological relations together withconvexity. We consider constraint networks whose nodes are regularregions (a regular region is one equal to the closure of itsinterior) and whose constraints have the following forms: (i)the eight ’’base relations‘‘ of [12], which describe binary topologicalrelations of containment and adjacency between regions; (ii)the predicate, ’’ X is convex.‘‘ We establish tightbounds on the computational complexity of this language: Determiningwhether such a constraint network is consistent is decidable,but essentially as hard as determining whether a set of comparablesize of algebraic constraints over the real numbers is consistent.We also show an important expressivity result for this language:If r and s are bounded, regular regionsthat are not related by an affine transformation, then they canbe distinguished by a constraint network. That is, there is aconstraint network and a particular node in that network suchthat there is a solution where the node is equal to r,but no solution where the node is equal to s.