Amortized efficiency of list update and paging rules
Communications of the ACM
On the performance of on-line algorithms for partition problems
Acta Cybernetica
Scheduling parallel machines on-line
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
An on-line scheduling heuristic with better worst case ratio than Graham's list scheduling
SIAM Journal on Computing
A better lower bound for on-line scheduling
Information Processing Letters
A lower bound for randomized on-line scheduling algorithms
Information Processing Letters
New algorithms for an ancient scheduling problem
Journal of Computer and System Sciences - Special issue on selected papers presented at the 24th annual ACM symposium on the theory of computing (STOC '92)
A better algorithm for an ancient scheduling problem
Journal of Algorithms
Better bounds for online scheduling
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
A lower bound for randomized on-line multiprocessor scheduling
Information Processing Letters
Randomized Algorithms for that Ancient Scheduling Problem
WADS '97 Proceedings of the 5th International Workshop on Algorithms and Data Structures
Probabilistic computations: Toward a unified measure of complexity
SFCS '77 Proceedings of the 18th Annual Symposium on Foundations of Computer Science
Approximation schemes for constrained scheduling problems
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
Scheduling on identical machines: How good is LPT in an on-line setting?
Operations Research Letters
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We present a deterministic online algorithm for scheduling two parallel machines when jobs arrive over time and show that it is (5-√5)/2 ≅ 1.38198-competitive. The best previously known algorithm is 3/2 -competitive. Our upper bound matches a previously known lower bound, and thus our algorithm has the best possible competitive ratio. We also present a lower bound of 1.21207 on the competitive ratio of any randomized online algorithm for any number of machines. This improves a previous result of 4-2√2 ≅ 1.17157.