| HAL-Inria | Publications, software ... of Inria's scientists |
Journal articles
Efficient Random-Walk Methods for Approximating Polytope Volume
Efficient Random-Walk Methods for Approximating Polytope Volume
Abstract : We experimentally study the fundamental problem of computing the volume of a convex polytope given as an intersection of linear inequalities. We implement and evaluate practical randomized algorithms for accurately approximating the polytope's volume in high dimensions (e.g. one hundred). To carry out this efficiently we experimentally correlate the effect of parameters, such as random walk length and number of sample points, on accuracy and runtime. Moreover, we exploit the problem's geometry by implementing an iterative rounding procedure, computing partial generations of random points and designing fast polytope boundary oracles. Our publicly available code is significantly faster than exact computation and more accurate than existing approximation methods. We provide volume approximations for the Birkhoff polytopes B 11 ,. .. , B 15 , whereas exact methods have only computed that of B 10 .
Cited literature [37 references]
https://hal.inria.fr/hal-01897272
Contributor : Ioannis Emiris Connect in order to contact the contributor
Submitted on : Sunday, October 28, 2018 - 12:43:28 PM
Last modification on : Friday, February 4, 2022 - 3:18:45 AM
Long-term archiving on: : Tuesday, January 29, 2019 - 12:50:14 PM
Contributor : Ioannis Emiris Connect in order to contact the contributor
Submitted on : Sunday, October 28, 2018 - 12:43:28 PM
Last modification on : Friday, February 4, 2022 - 3:18:45 AM
Long-term archiving on: : Tuesday, January 29, 2019 - 12:50:14 PM
File
1312.2873.pdf
Files produced by the author(s)