Volume Computation Using a Direct Monte Carlo Method
Volume 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 practice. On the other hand, applications emerging in computer science and other fields require practically effective methods to compute/estimate volume. This paper presents a practical Monte Carlo sampling algorithm on volume computation/estimation and a corresponding prototype tool is implemented. Preliminary experimental results on lower dimensional instances show a good approximation of volume computation for both convex and non-convex cases. While there is no theoretical performance guarantee, the method itself even works for the case when there is only a membership oracle, which tells whether a point is inside the geometric body or not, and no description of the actual geometric body is given.
KeywordsConvex Body Random Point Volume Computation Convex Polyhedron Prototype Tool
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