Decomposition of polytopes and polynomials
Abstract
Motivated by a connection with the factorization of multivariate polynomials, we study integral convex polytopes and their integral decompositions in the sense of the Minkowski sum. We first show that deciding decomposability of integral polygons is NPcomplete then present a pseudopolynomial time algorithm for decomposing polygons. For higher dimensional polytopes, we give a heuristic algorithm which is based upon projections and uses randomization. Applications of our algorithm include absolute irreducibility testing and factorization of polynomials via their Newton polytopes.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 December 2000
 arXiv:
 arXiv:math/0012099
 Bibcode:
 2000math.....12099G
 Keywords:

 Combinatorics;
 52B20;
 12Y05
 EPrint:
 29 pages, to appear in Discrete and Computational Geometry