An Improved Tight Closure Algorithm for Integer Octagonal Constraints
Abstract
Integer octagonal constraints (a.k.a. ``Unit Two Variables Per Inequality'' or ``UTVPI integer constraints'') constitute an interesting class of constraints for the representation and solution of integer problems in the fields of constraint programming and formal analysis and verification of software and hardware systems, since they couple algorithms having polynomial complexity with a relatively good expressive power. The main algorithms required for the manipulation of such constraints are the satisfiability check and the computation of the inferential closure of a set of constraints. The latter is called `tight' closure to mark the difference with the (incomplete) closure algorithm that does not exploit the integrality of the variables. In this paper we present and fully justify an O(n^3) algorithm to compute the tight closure of a set of UTVPI integer constraints.
 Publication:

arXiv eprints
 Pub Date:
 May 2007
 arXiv:
 arXiv:0705.4618
 Bibcode:
 2007arXiv0705.4618B
 Keywords:

 Computer Science  Data Structures and Algorithms;
 Computer Science  Computational Geometry;
 Computer Science  Logic in Computer Science
 EPrint:
 15 pages, 2 figures