 
Summary: BETTER BOUNDS FOR ONLINE SCHEDULING
SUSANNE ALBERSy
Abstract. 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, Fiat, Karlo and Vohra 3] gave a deterministic online
algorithm that is 1.986competitive. Karger, Phillips and Torng 11] 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 it equal to 1.837. In this paper we present
an improved deterministic online scheduling algorithm that is 1.923competitive, for all m 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 1.852competitive.
Key words. makespan minimization, online algorithm, competitive analysis
AMS subject classi cations. 68Q20, 68Q25, 90B35
1. Introduction. We study a classical problem in online scheduling. A sequence
of jobs must be scheduled on m identical parallel machines. Whenever a job arrives,
its processing time is known in advance, and the job must be scheduled immediately
on one of the machines, without knowledge of any future jobs. Preemption of jobs is
not allowed. The goal is to minimize the makespan, i.e., the completion time of the
