Upper Tail Analysis of Bucket Sort and Random Tries

Bucket Sort is known to run in expected linear time when the input keys are distributed independently and uniformly at random interval [0, 1). The analysis holds even a quadratic algorithm used sort each bucket. We show how obtain guarantees on running of that hold with very high probability. Specifically, we investigate asymptotic behavior exponent upper tail probability Sort. consider large additive deviations from expectation, form cn for enough (constant) c, where n number sorted.