Name
Abstract | ||
|---|---|---|
The volume is an important attribute of a convex body. In general, it is quite difficult to calculate the exact volume. But in many cases, it suffices to have an approximate value. Volume estimation methods for convex bodies have been extensively studied in theory, however, there is still a lack of practical implementations of such methods. In this paper, we present an efficient method which is based on the Multiphase Monte-Carlo algorithm to estimate volumes of convex polytopes. It uses the coordinate directions hit-and-run method, and employs a technique of reutilizing sample points. We also introduce a new result checking method for performance evaluation. The experiments show that our method can efficiently handle instances with dozens of dimensions with high accuracy. |
Year | DOI | Venue |
|---|---|---|
2014 | 10.1007/978-3-319-19647-3_6 | Lecture Notes in Computer Science |
Field | DocType | Volume |
Mathematical optimization,Convex body,Convex combination,Convex hull,Regular polygon,Polytope,Volume estimation,Proper convex function,Convex optimization,Mathematics | Journal | 9130 |
ISSN | Citations | PageRank |
0302-9743 | 1 | 0.37 |
References | Authors | |
7 | 2 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Cunjing Ge | 1 | 3 | 2.12 |
| Feifei Ma | 2 | 58 | 13.64 |