Abstract
A bin of capacity 1 and a finite sequence σ of items of sizes a 1,a 2,… are considered, where the items are given one by one without information about the future. An online algorithm A must irrevocably decide whether or not to put an item into the bin whenever it is presented. The goal is to maximize the number of items collected. A is f-competitive for some function f if n*(σ) ≤ f(n A (σ)) holds for all sequences σ, where n* is the (theoretical) optimum and n A the number of items collected by A.
A necessary condition on f for the existence of an f-competitive (possibly randomized) online algorithm is given. On the other hand, this condition is seen to guarantee the existence of a deterministic online algorithm that is “almost” f-competitive in a well-defined sense.
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References
U. Faigle, R. Garbe, and W. Kern [1996]-.Randomized online algorithms for maximizing busy time interval scheduling. Computing 56, 95–104.
E.J. Lipton and A. Tomkins [1994]: Online interval scheduling. Proceedings of the 5th Annual ACM-SIAM Symposium on Discrete Algorithms, Arlington, VA, 1994. ACM-SIAM, New York, 302–311.
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© 1997 Springer-Verlag Berlin Heidelberg
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Faigle, U., Kern, W. (1997). Packing a Bin Online to Maximize the Total Number of Items. In: Operations Research Proceedings 1996. Operations Research Proceedings, vol 1996. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-60744-8_12
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DOI: https://doi.org/10.1007/978-3-642-60744-8_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-62630-5
Online ISBN: 978-3-642-60744-8
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