A fast algorithm for generating a uniform distribution inside a high-dimensional polytope (Q5932766)

The paper presents a rejection free algorithm for the generation of uniformly distributed points \((x_1,x_2,\dots, x_m)\) , \(|x_i|< 1\) for all \(i\), satisfying the additional condition \(|x_i - x_k|< 1\) for all \(i,\;k\). The problem has to be solved during some simulation experiments in physics. An explicit formula for the complexity of the algoritm is developed. The complexity is linear in \(m\). The algoritm is exponentially better than the standard rejection algorithm and is more efficient than the rejection algorithm for \(m>4\).