Amortized efficiency of list update and paging rules
Communications of the ACM
Optimal Non-preemptive Semi-online Scheduling on Two Related Machines
MFCS '02 Proceedings of the 27th International Symposium on Mathematical Foundations of Computer Science
ESA '97 Proceedings of the 5th Annual European Symposium on Algorithms
The exact LPT-bound for maximizing the minimum completion time
Operations Research Letters
Semi on-line algorithms for the partition problem
Operations Research Letters
A polynomial-time approximation scheme for maximizing the minimum machine completion time
Operations Research Letters
Ordinal algorithms for parallel machine scheduling
Operations Research Letters
Semi-on-line scheduling with ordinal data on two uniform machines
Operations Research Letters
Optimal preemptive semi-online scheduling to minimize makespan on two related machines
Operations Research Letters
An Optimal On-Line Algorithm for Preemptive Scheduling on Two Uniform Machines in the lpNorm
AAIM '08 Proceedings of the 4th international conference on Algorithmic Aspects in Information and Management
A Lower Bound for the On-Line Preemptive Machine Scheduling with lpNorm
COCOON '08 Proceedings of the 14th annual international conference on Computing and Combinatorics
Approximation Algorithms for the Max-Min Allocation Problem
APPROX '07/RANDOM '07 Proceedings of the 10th International Workshop on Approximation and the 11th International Workshop on Randomization, and Combinatorial Optimization. Algorithms and Techniques
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In this paper, we consider an ordinal on-line scheduling problem. A sequence of n independent jobs has to be assigned non-preemptively to two uniformly related machines. We study two objectives which are maximizing the minimum machine completion time, and minimizing the l"p norm of the completion times. It is assumed that the values of the processing times of jobs are unknown at the time of assignment. However it is known in advance that the processing times of arriving jobs are sorted in a non-increasing order. We are asked to construct an assignment of all jobs to the machines at time zero, by utilizing only ordinal data rather than actual magnitudes of jobs. For the problem of maximizing the minimum completion time we first present a comprehensive lower bound on the competitive ratio, which is a piecewise function of machine speed ratio s. Then, we propose an algorithm which is optimal for any s=1. For minimizing the l"p norm, we study the case of identical machines (s=1) and present tight bounds as a function of p.