Details:
Title  A much better polynomial time approximation of consistency in the LR calculus.  Author(s)  Dominik Lücke, Michael Stillman  Type  Book, Chapter in Book, Conference Proceeding  Abstract  n the area of qualitative spatial reasoning, the LR calculus (a refinement of Ligozat's flipflop calculus) is a quite simple constraint calculus that forms the core of several orientation calculi like the Dipole calculi and the OPRA1 calculus by introducing the leftrightdichotomy.
For many qualitative spatial calculi, algebraic closure is applied as the standard polynomial time “decision” procedure. For a long time it was believed that this can decide the consistency of scenarios of the LR calculus. However, in [8] it was shown that algebraic closure is a bad approximation of consistency for LR scenarios: scenarios in the base relations “Left” and “Right” are always algebraically closed, no matter if those scenarios are consistent or not. So algebraic closure is completely useless here. Furthermore, in [15] it was proved that the consistency problem for any calculus with relative orientation containing the relations “Left” and “Right” is NPhard.
In this paper we propose a new and better polynomial time approximation procedure for this NPhard problem. It is based on the angles of triangles in the Euclidean plane. LR scenarios are translated to sets of linear inequalities over the real numbers. We evaluate the quality of this procedure by comparing it bot to the old approximation using algebraic closure and to the (exact but exponential time) Buchberger algorithm for Gröbner bases (used as a decision method).  ISBN  9781607506751/hbk; 97816 
URL 
http://ebooks.iospress.nl/publication/6267 
Language  English  Pages  175185  Publisher  Amsterdam: IOS Press  Year  2011  Edition  0  Translation 
No  Refereed 
No 
