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B. CHANDRA, Does randomization help in on-line bin packing?, Inform. Process. Lett., 43 (1992), pp. 15-19.

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New Bounds for Variable-Sized Online Bin Packing - Seiden, van Stee, Epstein (2003)   (Correct)

....that REVISED FIRST FIT has performance ratio formance ratio T5 and further showed that no online algorithm has performance ratio less than 32 [21] Brown [1] and Liang [14] independently improved this lower bound to 1.53635. This was subsequently improved by van Vliet to 1. 54014 [19] Chandra [2] shows that the preceding lower bounds also apply to randomized algorithms. Define ui =ui(ui 1) l, u=2, and 1.69103. Lee and Lee showed that the HARMONIC algorithm, which uses bounded space, achieves a performance ratio arbitrarily close to h [13] They further showed that no bounded space ....

B. CHANDRA, Does randomization help in on-line bin packing?, Inform. Process. Lett., 43 (1992), pp. 15-19.


On the Fractal Beauty of Bin Packing - Epstein, Seiden, van Stee (2001)   (Correct)

....[10] Yao showed that Revised First Fit has performance ratio 3 , and further showed that no online algorithm has performance ratio less than [20] Brown and Liang independently improved this lower bound to 1.53635 [1, 13] This was subsequently improved by van Vliet to 1. 54014 [18] Chandra [2] shows that the preceding lower bounds also apply to randomized algorithms. Define u i 1 = u i (u i Gamma 1) 1; u 1 = 2; and h1 = u i Gamma 1 1:69103: Lee and Lee showed that the Harmonic algorithm, which uses bounded space, achieves a performance ratio arbitrarily close to h1 ....

Chandra, B. Does randomization help in on-line bin packing? Information Processing Letters 43, 1 (Aug 1992), 15--19.


On the Fractal Beauty of Bin Packing - Epstein, Seiden, van Stee (2001)   (Correct)

....Yao showed that Revised First Fit has performance ratio 5 3 , and further showed that no online algorithm has performance ratio less than 3 2 [20] Brown and Liang independently improved this lower bound to 1.53635 [1, 13] This was subsequently improved by van Vliet to 1. 54014 [18] Chandra [2] shows that the preceding lower bounds also apply to randomized algorithms. Define u i 1 = u i (u i Gamma 1) 1; u 1 = 2; and h1 = 1 X i=1 1 u i Gamma 1 1:69103: Lee and Lee showed that the Harmonic algorithm, which uses bounded space, achieves a performance ratio arbitrarily close to ....

Chandra, B. Does randomization help in on-line bin packing? Information Processing Letters 43, 1 (Aug 1992), 15--19.


Best-Fit Bin-Packing with Random Order - Kenyon (1997)   (7 citations)  (Correct)

.... is 1:58 : 16] The quest for better algorithms was somewhat quelched by Yao s lower bound: no deterministic on line algorithm can have performance ratio better than 1:5 [19] This lower bound was later improved up to 1:54 : in [13, 6, 18] and proved to hold even for randomized algorithms [1]. The performance ratio has the drawback that for Best fit, the worst case sequences upon which it relies are very contrived and never occur in practice. These sequences are contrived in two ways: on the one hand, the values of the items inserted are very special, and on the other hand, they must ....

B. Chandra, Does randomization help in on-line binpacking ? IPL 43, 1, 15-19, 1992.

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