Using dual approximation algorithms for scheduling problems theoretical and practical results
Journal of the ACM (JACM)
On the performance of on-line algorithms for partition problems
Acta Cybernetica
New algorithms for an ancient scheduling problem
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
An on-line scheduling heuristic with better worst case ratio than Graham's list scheduling
SIAM Journal on Computing
On-line load balancing with applications to machine scheduling and virtual circuit routing
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
A lower bound for randomized on-line scheduling algorithms
Information Processing Letters
Better bounds for online scheduling
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
A better algorithm for an ancient scheduling problem
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Competitive routing of virtual circuits with unknown duration
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Online Load Balancing of Temporary Tasks
WADS '93 Proceedings of the Third Workshop on Algorithms and Data Structures
On-Line Load Balancing of Temporary Tasks on Identical Machines
ISTCS '97 Proceedings of the Fifth Israel Symposium on the Theory of Computing Systems (ISTCS '97)
SFCS '92 Proceedings of the 33rd Annual Symposium on Foundations of Computer Science
Semi on-line algorithms for the partition problem
Operations Research Letters
Ordinal On-Line Scheduling on Two Uniform Machines
COCOON '00 Proceedings of the 6th Annual International Conference on Computing and Combinatorics
Semi-online scheduling with decreasing job sizes
Operations Research Letters
Semi-on-line scheduling with ordinal data on two uniform machines
Operations Research Letters
Semi-on-line problems on two identical machines with combined partial information
Operations Research Letters
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We are given a sequence of items that can be packed into m unit size bins. In the classical bin packing problem we fix the size of the bins and try to pack the items in the minimum number of such bins. In contrast, in the bin-stretching problem we fix the number of bins and try to pack the items while stretching the size of the bins as least as possible. We present two on-line algorithms for the bin-stretching problem that guarantee a stretching factor of 5/3 for any number m of bins. We then combine the two algorithms and design an algorithm whose stretching factor is 1.625 for any m. The analysis for the performance of this algorithm is tight. The best lower bound for any algorithm is 4/3 for any m ≥ 2. We note that the bin-stretching problem is also equivalent to the classical scheduling (load balancing) problem in which the value of the makespan (maximum load) is known in advance.