Linear waste of best fit bin packing on skewed distributions

We prove that Best Fit bin packing has linear waste on the discrete distribution U{j, k} (where items are drawn uniformly from the set {1/k, 2/k, …, j/k}) for sufficiently large k when j = αk and 0.66 ≤ α < 2/3. Our results extend to continuous skewed distributions, where items are drawn uniformly on [0, a], for 0.66 ≤ a < 2/3. This implies that the expected asymptotic performance ratio of Best Fit is strictly greater than 1 for these distributions.