Priority algorithms for makespan minimization in the subset model

We continue the recent study of priority algorithms initiated by Borodin et al. [Proc. 13th ACM-SIAM Symp. on Discrete Algorithms, 2002, pp. 752-761]. The definition of a priority algorithm nicely captures the idea of a "greedy-like" type algorithm. While priority algorithms are applicable to many optimization problems, in this paper we consider the problem of makespan minimization in scheduling in the subset model. We show that by using a fixed priority algorithm one cannot achieve a considerable improvement over the approximation ratio given by the online greedy algorithm. Namely, we present an Ω(logm/loglogm) lower bound on the approximation ratio of any fixed priority algorithm where m is the number of machines.