Average Case Analysis of Bounded Space Bin Packing Algorithms

Naaman, Nir; Rom, Raphaël

doi:10.1007/s00453-007-9073-y

Cited by 8 publications

(5 citation statements)

References 24 publications

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“…A proof of a similar statement can be found in the extended version of [16]. For our purposes it is easier to deal with AECR(DNF, F ), so we will only mention this measure in the following.…”

Section: Basic Statementsmentioning

confidence: 83%

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: Basic Statementsmentioning

confidence: 83%

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

Fischer

Röglin

2016

LATIN 2016: Theoretical Informatics

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“…Ramanan [Ram89] applies a similar analysis to a variant of NextFit called SmartNextFit. Recently, Naaman and Rom [NR08] used a Markov chain approach to analyze the asymptotic expected performance ratio for several bounded-space bin packing algorithms. An alternative way of measuring the performance of bin packing algorithms is to consider the growth of the waste, which is the bin capacity that remains unutilized by the bin packing algorithm.…”

Section: Related Applications Of Markov Chains and Stochastic Dominancementioning

confidence: 99%

Online Optimization: Probabilistic Analysis and Algorithm Engineering

Hiller

2011

Operations Research Proceedings

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“…However, it is also true that worst-case analysis is often criticized as too pessimistic, and average-case analysis has always been an interesting research target. For online algorithms as well, several objective functions as presented above have recently appeared in the literature [FI05,PS06,Bec04,SSS06,NR08,GGLS08]. Our current problem involves a lot of human activities; it seems especially interesting to make an analysis under proper input distributions.…”

Section: Introductionmentioning

confidence: 99%

“…OPT] make no difference as far as we consider the asymptotic ratio for a sufficiently long input sequence[NR08].Garg et al recently pointed out the difference between E ALG OPT and E[ALG] E[OPT] for the online Steiner tree problem: To obtain an upper bound of E ALG OPT requires a scenario-wise comparison independently of results for…”

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confidence: 99%

Average-case competitive analyses for one-way trading

2009

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Consider a trader who exchanges one dollar into yen and assume that the exchange rate fluctuates within the interval [m, M ]. The game ends without advance notice, then the trader is forced to exchange all the remaining dollars at the minimum rate m. El-Yaniv et al. presented the optimal worst-case threat-based strategy for this game [EFKT01]. In this paper, under the assumption that the distribution of the maximum exchange rate is known, we provide average-case analyses using all the reasonable optimization measures and derive different optimal strategies for each of them. Remarkable differences in behavior are as follows: Unlike other strategies, the average-case threat-based strategy that minimizes E[OPT/ALG] exchanges little by little. The maximization of E[ALG/OPT] and the minimization of E[OPT]/E[ALG] lead to similar strategies in that both exchange all at once. However, their timing is different. We also prove minimax theorems with respect to each objective function.

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Average Case Analysis of Bounded Space Bin Packing Algorithms

Cited by 8 publications

References 24 publications

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

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

Online Optimization: Probabilistic Analysis and Algorithm Engineering

Average-case competitive analyses for one-way trading

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