A deterministic polynomial-time algorithm for approximating mixed discriminant and mixed volume

Leonid Gurvits, Alex Samorodnitsky

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

14 Scopus citations

Abstract

We present a deterministic polynomial algorithm that computes the mixed discriminant of an n-tuple of positive semidefinite matrices to within a multiplicative factor of en. 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. We obtain tight upper and lower bounds on the mixed discriminant of doubly stochasic n-tuples, proving a conjecture of Bapat, and generalizing the van der Waerden - Falikman - Egorychev theorem. As a corollary, we obtain a deterministic polynomial algorithm that computes the mixed volume of n convex bodies in Rn to within a multiplicative factor of nO(n). This answers a question of Dyer, Gritzmann and Hufnagel.

Original languageAmerican English
Title of host publicationProceedings of the 32nd Annual ACM Symposium on Theory of Computing, STOC 2000
Pages48-57
Number of pages10
DOIs
StatePublished - 2000
Externally publishedYes
Event32nd Annual ACM Symposium on Theory of Computing, STOC 2000 - Portland, OR, United States
Duration: 21 May 200023 May 2000

Publication series

NameProceedings of the Annual ACM Symposium on Theory of Computing
ISSN (Print)0737-8017

Conference

Conference32nd Annual ACM Symposium on Theory of Computing, STOC 2000
Country/TerritoryUnited States
CityPortland, OR
Period21/05/0023/05/00

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