An Algebra for Cyclic Ordering of 2D Orientations

Wedefine an algebra of ternary relations for cyclic ordering of 2Dorientations. Thealgebra (1) is a refinement of the CYCORDtheory; (2) contains 24 atomic relations, hence 224 general relations, of which the usual CYCORDrelation is a particular relation; and (3) is NP-complete,which is not surprising since the CYCORDtheory is. Wethen provide: (1) a constraint propagation algorithm for the algebra, which we show is polynomial, and complete for a subclass including all atomic relations; (2) a proof that another subclass, expressing only information on parallel orientations, is NP-complete;and (3) a solution search algorithm for general problem expressed in the algebra.

• Type: Conference
• Year: 1998
• Where: AAAI
• Authors: Amar Isli, Anthony G. Cohn
• Keywords: AAAI 1998, Atomic Relations, Constraint Propagation Algorithm, Intelligent Agents, Ternary Relations