Approximation schemes for scheduling
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
All-Norm Approximation Algorithms
SWAT '02 Proceedings of the 8th Scandinavian Workshop on Algorithm Theory
Convex programming for scheduling unrelated parallel machines
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Approximation Algorithms for Scheduling on Multiple Machines
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Load balancing of temporary tasks in the lp norm
Theoretical Computer Science - Approximation and online algorithms
Optimal on-line algorithms for the uniform machine scheduling problem with ordinal data
Information and Computation
Optimal preemptive scheduling for general target functions
Journal of Computer and System Sciences
Preemptive on-line scheduling for two uniform processors
Operations Research Letters
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One of the basic and fundamental problems in scheduling is to minimize the machine completion time vector in the 驴pnorm (a direct extension of the l驴norm: the makespan) on uniform parallel machines. We concentrate on the on-line and preemptive version of this problem where jobs arrive one by one over a list and are allowed to be preempted. We present a best possible deterministic on-line scheduling algorithm along with a matching lower bound when there are two machines, generalizing existing results for the identical machines scheduling problem in the literature. The main difficulty in the design of the algorithm and the analysis of the resultant competitive ratio as well as the proof of the lower bound is that the competitive ratio is only known to be the root of some equation systems, which admits no analytic solution--a distinct feature from most existing literature on competitive analysis. As a consequence, we develop some new ideas to tackle this difficulty. Specifically we need to exploit the properties of the equations system that defines the competitive ratio.