Discrete & Computational Geometry

, Volume 26, Issue 1, pp 89–104 | Cite as

Decomposition of Polytopes and Polynomials

  • S. Gao
  • A. G. B. Lauder


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 NP-complete then present a pseudo-polynomial-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 algorithms include absolute irreducibility testing and factorization of polynomials via their Newton polytopes.

Copyright information

© Springer-Verlag New York Inc. 2001

Authors and Affiliations

  • S. Gao
    • 1
  • A. G. B. Lauder
    • 2
  1. 1.Department of Mathematical Sciences, Clemson University, Clemson, SC 29634-0975, USA sgao@math.clemson.eduUSA
  2. 2.Mathematical Institute, Oxford University, Oxford OX1 3LB, England

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