A random polynomial time algorithm for well-rounding convex bodies

We present a random polynomial time algorithm for well-rounding convex bodies K in the following sense: Given K and > 0, the algorithm, with probability at least 1 — , computes two simplices * and **, where ** is the blow up of * from its center by a factor of n + 3, such that \ud Δ*K and vol (K/Δ**)≤ volK. The running time is polynomial in 1 / and L, the size of the input K