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@TechReport{BagnaraHZ07TRb,
  Author = "R. Bagnara and P. M. Hill and E. Zaffanella",
  Title = "An Improved Tight Closure Algorithm
           for Integer Octagonal Constraints",
  Number = 467,
  Type = "Quaderno",
  Institution = "Dipartimento di Matematica, Universit\`a di Parma, Italy",
  Year = 2007,
  Note = "Available at \url{http://www.cs.unipr.it/Publications/}.
          Also published as {\tt arXiv:0705.4618v2 [cs.DS]},
          available from \url{http://arxiv.org/}.",
  Abstract = "Integer octagonal constraints (a.k.a.\ \emph{Unit Two
              Variables Per Inequality} or \emph{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 \emph{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.  result
              in important contributions are highlighted.",
}