The convex hull of a regular set of integer vectors is polyhedral and effectively computable

Alain Finkel (1) , Jérôme Leroux (2)

1 LSV - Laboratoire Spécification et Vérification [Cachan]
2 LaBRI - Laboratoire Bordelais de Recherche en Informatique

Number Decision Diagrams (NDD) provide a natural finite symbolic representation for regular set of integer vectors encoded as strings of digit vectors (least or most significant digit first). The convex hull of the set of vectors represented by a NDD is proved to be an effectively computable convex polyhedron.

Mots clés: approximation algorithms; polyhedral convex set; presburger arithmetic; symbolic representation

Domaines: Géométrie algorithmique [cs.CG]; Algorithme et structure de données [cs.DS]; Logique en informatique [cs.LO]

Alain Finkel, Jérôme Leroux. The convex hull of a regular set of integer vectors is polyhedral and effectively computable. Information Processing Letters, 2005, 96 (1), pp.30 - 35. ⟨10.1016/j.ipl.2005.04.004⟩. ⟨hal-00345982⟩