Practical Polytope Volume Approximation

International audienceWe 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

volume computation using a direct monte carlo method

Univ Alberta, Dept Comp Sci, Informat Circle Res ExcellenceVolume computation is a traditional, extremely hard but highly demanding task. It has been widely studied and many interesting theoretical results are obtained in recent years. But very little attention is paid to put theory into use in pract