J. K. Lenstra, D. B. Shmoys, and E. Tardos. Approximation algorithms for scheduling unrelated parallel machines. Math. Programming, 46(3, (Ser. A)):259--271, 1990. Home/Search Document Not in Database Summary Related Articles Check |
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All-norm Approximation Algorithms - Yossi Azar Leah (2002) (1 citation) (Correct)
....we consider the problem of scheduling in the restricted assignment model, where there are m machines and n jobs, each is associated with a subset of the machines and should be assigned to one of them. Previous work considered approximation algorithms for each norm separately. Lenstra et al. [11] showed a 2 approximation algorithm for the problem with respect to the # norm. For any fixed # p norm the previously known approximation algorithm has a performance of #(p) We provide an all norm 2 approximation polynomial algorithm for the restricted assignment problem. On the other hand, ....
....hence the best we can hope for (independent of the computational power) is an all norm # approximation, when # is constant. Moreover, from the computational point of view, we can not expect to achieve an all norm approximation polynomial algorithm with ratio better than 3 2 since Lenstra et al. [11] proved a 3 2 lower bound on the approx2 imation ratio of any polynomial algorithm for the makespan alone (assuming P #= NP ) Lenstra et al. 11] and Shmoys and Tardos [15] presented a 2 approximation algorithm for the makespan, however their algorithm does not guarantee any constant ....
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J.K. Lenstra, D.B. Shmoys, and E. Tardos. Approximation algorithms for scheduling unrelated parallel machines. Math. Prog., 46:259--271, 1990.
Temporary Tasks Assignment Resolved - Armon, Azar, Epstein, Regev (Correct)
.... tasks, the tasks do not depart (all the departure times equal 1) Horowitz and Sahni presented an FPTAS for permanent tasks assignment on a xed number of unrelated machines (i.e. the number of machines is not a part of the input) 17] A PTAS for this problem was also presented by Lenstra et al. [19]. For permanent tasks assignment on an arbitrary number of unrelated machines, Lenstra et al. 19] and Shmoys and Tardos [22] presented algorithms with an approximation ratio of 2. In addition, Lenstra et al. proved that no algorithm can reach an approximationratio better than for the arbitrary ....
.... FPTAS for permanent tasks assignment on a xed number of unrelated machines (i.e. the number of machines is not a part of the input) 17] A PTAS for this problem was also presented by Lenstra et al. 19] For permanent tasks assignment on an arbitrary number of unrelated machines, Lenstra et al. [19] and Shmoys and Tardos [22] presented algorithms with an approximation ratio of 2. In addition, Lenstra et al. proved that no algorithm can reach an approximationratio better than for the arbitrary number of machines case, unless P = NP [19] Unlike the permanent case, solving the problem of ....
[Article contains additional citation context not shown here]
J.K. Lenstra, D.B. Shmoys, and E. Tardos. Approximation algorithms for scheduling unrelated parallel machines. Math. Prog., 46:259-271, 1990.
Dependent Rounding in Bipartite Graphs - Gandhi, Khuller, Parthasarathy.. (2002) (3 citations) (Correct)
....set cover problem. As a corollary to our rounding procedure, for the weighted version, we obtain a 2 approximate solution in which a vertex v is used at most 2b v times to cover edges. d) Scheduling on unrelated parallel machines. One of the early LP rounding results in scheduling is as follows [15]. Suppose we have a set of jobs and a set of machines. Each job j must be processed on some machine; processing it on machine i involves a load of p i;j on machine i. Suppose we wish to find a schedule that minimizes the makespan: the maximum total load on any machine. A 2 approximation, as well ....
....be processed on some machine; processing it on machine i involves a load of p i;j on machine i. Suppose we wish to find a schedule that minimizes the makespan: the maximum total load on any machine. A 2 approximation, as well as a proof that a 1:5 approximation would imply P = NP , are shown in [15]. Since then, the approximability of this problem has been open. Chekuri and Khanna [4] show that it is possible to obtain a schedule in which the makespan is at most T but each job gets scheduled with a probability 1=2. Their algorithm uses the algorithm in [15] However, it is not clear if we ....
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J. K. Lenstra, D. B. Shmoys and E. Tardos. Approximation algorithms for scheduling unrelated parallel machines. Mathematical Programming, 46:259--271, 1990.
Fairness in Routing and Load Balancing - Jon Kleinberg Yuval (1999) (15 citations) Self-citation (Tardos) (Correct)
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J.K. Lenstra, D. Shmoys, E. Tardos, "Approximation algorithms for scheduling unrelated parallel machines," Proc. 28th IEEE FOCS, 1987.
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J. K. Lenstra, D. B. Shmoys, and E. Tardos. Approximation algorithms for scheduling unrelated parallel machines. Math. Programming, 46(3, (Ser. A)):259--271, 1990.
Graph Orientation Algorithms to - Minimize The Maximum (Correct)
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Lenstra, J.K., Shmoys, D.B., & Tardos, E. (1990), `Approximation algorithms for scheduling unrelated parallel machines,' Mathematical Programming 46 (3), 259--271.
On the Complexity of Cell Flipping in Permutation.. - Golumbic, Kaplan, Verbin (2005) (Correct)
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J. K. Lenstra, D. B. Shmoys, and E. Tardos. Approximation algorithms for scheduling unrelated parallel machines. Mathematical Programming, 46:259-271, 1990. An earlier version of this appeared in the Proceedings of the 28 Annual IEEE Symposium on Foundations of Computer Science.
Cell Flipping in Permutation Diagrams - Golumbic, Kaplan, Verbin (2003) (Correct)
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J. K. Lenstra, D. B. Shmoys, and E. Tardos. Approximation algorithms for scheduling unrelated parallel machines. Mathematical Programming, 46:259-271, 1990. An earlier version of this appeared in the Proceedings of the 28 Annual IEEE Symposium on Foundations of Computer Science. 21
The Load Rebalancing Problem - Aggarwal, Motwani, Zhu (2003) (1 citation) (Correct)
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J.K. Lenstra, D. Shmoys, and E. Tardos. Approximation Algorithms for Scheduling Unrelated Parallel Machines. Mathematical Programming, 46(1990):259--271.
Load Balancing In Hop-By-Hop Routing With And Without Traffic.. - Wang (2003) (Correct)
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J.K. Lenstra, D. Shmoys, and E. Tardos. Approximation algorithms for scheduling unrelated parallel machines. In 28th IEEE FOCS, 1987.
On Approximately Fair Allocations of Indivisible Goods - Richard Lipton Evangelos (2004) (1 citation) (Correct)
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J. K. Lenstra, D. B. Shmoys, E. Tardos (1982). Approximation algorithms for scheduling unrelated parallel machines. Mathematical Programming, 46, 259-271.
Experimental Evaluation of Approximation Algorithms for.. - Kolliopoulos, Stein (1999) (Correct)
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J. K. Lenstra, D. B. Shmoys, and ' E. Tardos. Approximation algorithms for scheduling unrelated parallel machines. Mathematical Programming, 46:259--271, 1990.
Algorithms for Flow Time Scheduling - Bansal (2003) (Correct)
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J. Lenstra, D. Shmoys, and E. Tardos. Approximation algorithms for scheduling unrelated parallel machines. Mathematical Programming, 46:259--271, 1990.
Approximation Algorithms for Single-Source Unsplittable Flow - Kolliopoulos, Stein (1997) (2 citations) (Correct)
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J. K. Lenstra, D. B. Shmoys, and E. Tardos, Approximation algorithms for scheduling unre- lated parallel machines, Mathematical Programming, 46 (
Scheduling Malleable Parallel Tasks: An Asymptotic Fully.. - Jansen (Correct)
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J.K. Lenstra, D.B. Shmoys and E. Tardos, Approximation algorithms for scheduling unrelated parallel machines, Mathematical Programming, 24 (1990), 259-272.
Implementing Approximation Algorithms for the Single-Source.. - Jingde Du And (Correct)
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J. K. Lenstra, D. B. Shmoys, and E. Tardos. Approximation algorithms for scheduling unrelated parallel machines. Mathematical Programming 46, 259--271, 1990.
Improved Approximation Algorithms for Minimum-Space.. - Dean, Goemans (2003) (1 citation) (Correct)
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J.K. Lenstra, D.B. Shmoys, and E. Tardos (1990). \Approximation algorithms for scheduling unrelated parallel machines". Mathematical Programming 46, 259-271.
All-Norm Approximation for Scheduling on Identical Machines - Azar, Taub (2004) (1 citation) (Correct)
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J.K. Lenstra, D.B. Shmoys, and E. Tardos. Approximation algorithms for scheduling unrelated parallel machines. Math. Prog., 46:259-271, 1990.
Approximation Algorithms for Disjoint Paths Problems - Kleinberg (1996) (62 citations) (Correct)
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J.K. Lenstra, D.B. Shmoys, ' E. Tardos, "Approximation algorithms for scheduling unrelated parallel machines," Proc. 28th IEEE Symp. on Foundations of Computer Science, 1987.
Exact and Approximation Algorithms for Network Flow and.. - Kolliopoulos (1998) (2 citations) (Correct)
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J. K. Lenstra, D. B. Shmoys, and E. Tardos. Approximation algorithms for scheduling unrelated parallel machines. Mathematical Programming, 46:259-- 271, 1990.
Load Balancing in Multimedia Servers - Aerts, Korst, Verhaegh (2000) (1 citation) (Correct)
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J.K. Lenstra, D.B. Shmoys, and E. Tardos, (1990) Approximation algorithms for scheduling unrelated parallel machines, Mathematical Programming 46, 259-270.
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J. K. Lenstra, D. B. Shmoys and E. Tardos, Approximation algorithms for scheduling unrelated parallel machines, Mathematical Programming, 24 (1990), 259-272.
Approximation Schemes for Flow Time on Multiple Machines - Bansal (2003) (Correct)
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J. Lenstra, D. Shmoys, and E. Tardos. Approximation algorithms for scheduling unrelated parallel machines. Mathematical Programming, 46:259-271, 1990.
Algorithms for Flow Time Scheduling - Bansal (Correct)
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J. Lenstra, D. Shmoys, and E. Tardos. Approximation algorithms for scheduling unrelated parallel machines. Mathematical Programming, 46:259-271, 1990.
The Load Rebalancing Problem - Aggarwal, Motwani, Zhu (2003) (1 citation) (Correct)
No context found.
J.K. Lenstra, D. Shmoys, and E. Tardos. Approximation Algorithms for Scheduling Unrelated Parallel Machines. Mathematical Programming, 46(1990):259--271.
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