Online bin covering: Expectations vs. guarantees

Christ, Marie G.; Favrholdt, Lene M.; Larsen, Kim S.

doi:10.1016/j.tcs.2014.06.029

Cited by 10 publications

(15 citation statements)

References 27 publications

(48 reference statements)

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“…Using ideas of Kenyon [11], it follows that AAPR(DNF) ≥ RR(DNF). We show that RR(DNF) ≤ AAPR(DNF) ≤ 2 /3, which improves a result by Christ et al [3] who proved that RR(DNF) ≤ 4 /5. To the best of our knowledge the bound by Christ et al is the only non-trivial result about the random-order ratio of DNF in the literature.…”

Section: Introductionsupporting

confidence: 89%

“…The asymptotic random-order ratio for bin covering and bin packing has been introduced in [3] and [11], respectively. All definitions above can also be adapted to the bin packing problem; we only have to replace inf and lim inf by sup and lim sup, respectively.…”

Section: Definitionmentioning

confidence: 99%

“…The (asymptotic) competitive ratio of DNF is 1 /2 [2], which is best possible for deterministic online algorithms [7]. In fact, all deterministic online algorithms that do not add items to a bin that is already covered and have at most a constant number of open bins at any point in time have a competitive ratio of exactly 1 /2 [3]. Since competitive analysis does not yield much insight for bin covering, alternative measures have been suggested.…”

Section: Introductionmentioning

confidence: 99%

“…Since competitive analysis does not yield much insight for bin covering, alternative measures have been suggested. Most notably are probabilistic models in which the item sizes are drawn at random from a fixed distribution [5] or in which the item sizes are adversarial but the items arrive in random order [3].…”

Section: Introductionmentioning

confidence: 99%

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Probabilistic Analysis of the Dual Next-Fit Algorithm for Bin Covering

Fischer

Röglin

2016

LATIN 2016: Theoretical Informatics

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Abstract. In the bin covering problem, the goal is to fill as many bins as possible up to a certain minimal level with a given set of items of different sizes. Online variants, in which the items arrive one after another and have to be packed immediately on their arrival without knowledge about the future items, have been studied extensively in the literature. We study the simplest possible online algorithm Dual Next-Fit, which packs all arriving items into the same bin until it is filled and then proceeds with the next bin in the same manner. The competitive ratio of this and any other reasonable online algorithm is 1/2. We study Dual Next-Fit in a probabilistic setting where the item sizes are chosen i.i.d. according to a discrete distribution and we prove that, for every distribution, its expected competitive ratio is at least 1/2 + ǫ for a constant ǫ > 0 independent of the distribution. We also prove an upper bound of 2/3 and better lower bounds for certain restricted classes of distributions. Finally, we prove that the expected competitive ratio equals, for a large class of distributions, the random-order ratio, which is the expected competitive ratio when adversarially chosen items arrive in uniformly random order.

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Section: Introductionsupporting

confidence: 89%

Section: Definitionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Probabilistic Analysis of the Dual Next-Fit Algorithm for Bin Covering

Fischer

Röglin

2016

LATIN 2016: Theoretical Informatics

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“…Random-order analysis has also been applied to other problems, e.g., knapsack [7], bipartite matching [43,35], scheduling [60,42], bin covering [30,41], and facility location [57]. However, the analysis is often rather challenging, and in [50], a simplified version of the random-order ratio is used for bin packing.…”

Section: The Random-order Ratiomentioning

confidence: 99%