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New Software and Platforms
New Results
Bibliography
New Software and Platforms
New Results
Bibliography


Section: New Results

Efficient Random-Walk Methods for Approximating Polytope Volume

Participant : Ioannis Emiris.

In [5] 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 of order 11 to 15, whereas exact methods have only computed that for order 10.

This is a joint work with Vissarion Fisikopoulos (Oracle Corp., Athens, Greece).