Better Bounds for Online Scheduling

We study a classical problem in online scheduling. A sequence of jobs must be scheduled on m identical parallel machines. As each job arrives, its processing time is known. The goal is to minimize the makespan. Bartal et al. [ J. Comput. System Sci., 51 (1995), pp. 359--366] gave a deterministic online algorithm that is 1.986-competitive. Karger, Phillips, and Torng [ J. Algorithms, 20 (1996), pp. 400--430] generalized the algorithm and proved an upper bound of 1.945. The best lower bound currently known on the competitive ratio that can be achieved by deterministic online algorithms is equal to 1.837. In this paper we present an improved deterministic online scheduling algorithm that is 1.923-competitive; for all $m\geq 2$. The algorithm is based on a new scheduling strategy, i.e., it is not a generalization of the approach by Bartal et al. Also, the algorithm has a simple structure. Furthermore, we develop a better lower bound. We prove that, for general m, no deterministic online scheduling algorithm can be better than 1.852-competitive.