A random polynomial time algorithm for well-rounding convex bodies

Abstract

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