Abstract
We present a deterministic polynomial-time algorithm that computes the mixed discriminant of an n -tuple of positive semidefinite matrices to within an exponential multiplicative factor. To this end we extend the notion of doubly stochastic matrix scaling to a larger class of n -tuples of positive semidefinite matrices, and provide a polynomial-time algorithm for this scaling. As a corollary, we obtain a deterministic polynomial algorithm that computes the mixed volume of n convex bodies in R n to within an error which depends only on the dimension. This answers a question of Dyer, Gritzmann and Hufnagel. A ``side benefit'' is a generalization of Rado's theorem on the existence of a linearly independent transversal.
Article PDF
Similar content being viewed by others
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Gurvits, Samorodnitsky A Deterministic Algorithm for Approximating the Mixed Discriminant and Mixed Volume, and a Combinatorial Corollary. Discrete Comput Geom 27, 531–550 (2002). https://doi.org/10.1007/s00454-001-0083-2
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00454-001-0083-2