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Integer octagonal constraints (a.k.a. ``Unit Two Variables Per Inequality''or ``UTVPI integer constraints'') constitute an interesting class ofconstraints for the representation and solution of integer problems in thefields of constraint programming and formal analysis and verification ofsoftware and hardware systems, since they couple algorithms having polynomialcomplexity with a relatively good expressive power. The main algorithmsrequired for the manipulation of such constraints are the satisfiability checkand the computation of the inferential closure of a set of constraints. Thelatter is called `tight' closure to mark the difference with the (incomplete)closure algorithm that does not exploit the integrality of the variables. Inthis paper we present and fully justify an O(n^3) algorithm to compute thetight closure of a set of UTVPI integer constraints.

An Improved Tight Closure Algorithm for Integer Octagonal Constraints