  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. The experiments show that our
method can efficiently handle instances with dozens of dimensions with high
accuracy.
