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Best-fit bin-packing with random order

Abstract : Best-fit is the best known algorithm for on-line bin-packing, in the sense that no algorithm is known to behave better both in the worst case (when Best-fit has performance ratio 1.7) and in the average uniform case, with items drawn uniformly in the interval [ 0, 1]. In practical applications, Best-fit appears to perform within a few percent of optimal. In this paper, we study the expected performance ratio, taking the worst-case multiset of items L$, and assuming that the elements of L are inserted in random order, with all permutations equally likely. We show a lower bound of 1.07... and an upper bound of 1.5 on the random order performance ratio of Best-fit. The upper bound contrasts with the result that in the worst case, any (deterministic or randomized) on-line bin-packing algorithm has performance ratio at least 1.54....
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Submitted on : Wednesday, April 17, 2019 - 9:12:09 AM
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Claire Kenyon. Best-fit bin-packing with random order. [Research Report] LIP RR-1995-19, Laboratoire de l'informatique du parallélisme. 1995, 2+12p. ⟨hal-02102019⟩



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