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Article Dans Une Revue Mathematics of Computation Année : 2011

How to Integrate a Polynomial over a Simplex

Résumé

This paper settles the computational complexity of the problem of integrating a polynomial function f over a rational simplex. We prove that the problem is NP-hard for arbitrary polynomials via a generalization of a theorem of Motzkin and Straus. On the other hand, if the polynomial depends only on a fixed number of variables, while its degree and the dimension of the simplex are allowed to vary, we prove that integration can be done in polynomial time. As a consequence, for polynomials of fixed total degree, there is a polynomial time algorithm as well. We conclude the article with extensions to other polytopes and discussion of other available methods.
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Dates et versions

hal-00320882 , version 1 (11-09-2008)

Identifiants

Citer

Velleda Baldoni, Nicole Berline, Jesús A. de Loera, Matthias Köppe, Michèle Vergne. How to Integrate a Polynomial over a Simplex. Mathematics of Computation, 2011, 80 (273), pp.297-325. ⟨10.1090/S0025-5718-2010-02378-6⟩. ⟨hal-00320882⟩
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