Domination analysis for minimum multiprocessor scheduling

Let P be a combinatorial optimization problem, and let A be an approximation algorithm for P . The domination ratio domr(A, s) is the maximal real q such that the solution x(I) obtained by A for any instance I of P of size s is not worse than at least the fraction q of the feasible solutions of I. We say that P admits an Asymptotic Domination Ratio One (ADRO) algorithm if there is a polynomial time approximation algorithm A for P such that lims→∞ domr(A, s) = 1. Alon, Gutin and Krivelevich (J. Algorithms 50 (2004), 118–131) proved that the partition problem admits an ADRO algorithm. We extend their result to the minimum multiprocessor scheduling problem.