Convergence of optimal stochastic bin packing

Abstract

Consider independent identically distributed random variables ( X i ) valued in [0,1]. Let B(n) be the optimal (minimum) number of unit size bins needed to pack n items of size X 1, X 2,…, X n . We prove that there exists a numerical constant C such that for t > 0, Pr(∣B(n)−E(B(n))∣>t n )≤ C exp(− t). The constant C does not depend on the distribution of X.