Reproduce “An $\mathsf{FPRAS}$ for Mixed Volumes” on OpenResearch
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About this paper
Xiaoyu Chen, Kuikui Liu
The authors give the first FPRAS for mixed volume of n arbitrary compact convex sets in R^n supplied through weak-membership oracles. They smooth and rebalance the inputs, then sample using a mixed-discriminant approximation. It achieves relative error ε with probability at least 1−δ in polynomial oracle-call and bit-operation complexity, establishing a theoretical guarantee rather than practical speed.
Summary by alphaXiv.
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