Probabilistic Analysis of Online Bin Coloring Algorithms Via Stochastic Comparison

Hiller, Benjamin; Vredeveld, Tjark

doi:10.1007/978-3-540-87744-8_44

Cited by 9 publications

(13 citation statements)

References 24 publications

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“…We show that, according to the strict relative worst-order ratio, GF is better than OB. Interestingly, a related result was given by Hiller and Vredeveld [15] who showed that GF is better than OB, using probabilistic analysis.…”

Section: Bin Coloringmentioning

confidence: 80%

“…The bin covering problem [1,11,8,15] is in some sense the opposite of the bin packing problem as we now want to maximize the number of bins containing items of a total size of at least one. The Harmonic algorithms for this problem are the same as for standard bin packing, except that a bin is closed only when the total size of the items in the bin reaches at least one.…”

Section: Bin Coveringmentioning

confidence: 99%

“…We further consider a maximization variant called bin covering [1,9,11,8,15]. Here, the goal is to maximize the number of bins with a total size of items of at least 1. In open-end bin packing [24] a bin is allowed to contain items of total size larger than 1, as long the items assigned to the bin, except for the last one, have a total size strictly smaller than 1.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Comparing online algorithms for bin packing problems

Epstein

Favrholdt

Kohrt

2009

J Sched

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The relative worst-order ratio is a measure of the quality of online algorithms. In contrast to the competitive ratio, this measure compares two online algorithms directly instead of using an intermediate comparison with an optimal offline algorithm. In this paper, we apply the relative worst-order ratio to online algorithms for several common variants of the bin packing problem. We mainly consider pairs of algorithms that are not distinguished by the competitive ratio and show that the relative worst-order ratio prefers the intuitively better algorithm of each pair.

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Section: Bin Coloringmentioning

confidence: 80%

Section: Bin Coveringmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Comparing online algorithms for bin packing problems

Epstein

Favrholdt

Kohrt

2009

J Sched

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show abstract

“…It is known that for both paging anf list update, randomization helps in inproving the performance of algorithms, and a variety of randomized algorithms have been proposed and analyzed. Very recently, Hiller and Vredeveld [23] use the notion of stochastic dominance in the context of probabilistic analysis of online bin coloring algorithms. We believe that both these two types of analysis could be useful in studying the effect of randomization in online computation, since they are closely related.…”

Section: Discussionmentioning

confidence: 99%

Paging and list update under bijective analysis

Angelopoulos

Schweitzer

2013

J. ACM

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It has long been known that for the paging problem in its standard form, competitive analysis cannot adequately distinguish algorithms based on their performance: there exists a vast class of algorithms which achieve the same competitive ratio, ranging from extremely naive and inefficient strategies (such as Flush-When-Full), to strategies of excellent performance in practice (such as Least-Recently-Used and some of its variants). A similar situation arises in the list update problem: in particular, under the cost formulation studied by Martínez and Roura [TCS 2000] and Munro [ESA 2000] every list update algorithm has, asymptotically, the same competitive ratio. Several refinements of competitive analysis, as well as alternative performance measures have been introduced in the literature, with varying degrees of success in narrowing this disconnect between theoretical analysis and empirical evaluation.In this paper we study these two fundamental online problems under the framework of bijective analysis [Angelopoulos, López-Ortiz, SODA 2007 and LATIN 2008]. This is an intuitive technique which is based on pairwise comparison of the costs incurred by two algorithms on sets of request sequences of the same size. Coupled with a well-established model of locality of reference due to Albers, Favrholdt and Giel [JCSS 2005], we show that LeastRecently-Used and Move-to-Front are the unique optimal algorithms for paging and list update, respectively. Prior to this work, only measures based on average-cost analysis have separated LRU and MTF from all other algorithms. Given that bijective analysis is a fairly stringent measure (and also subsumes average-cost analysis), we prove that in a strong sense LRU and MTF stand out as the best (deterministic) algorithms.

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“…Very recently, Hiller and Vredeveld [19] use the notion of stochastic dominance in the context of probabilistic analysis of online bin coloring algorithms. We believe that both these two types of analysis could be useful in studying the effect of randomization in online computation, since they are closely related.…”

Section: Future Workmentioning

confidence: 99%

Paging and List Update under Bijective Analysis

Angelopoulos¹,

Schweitzer²

2009

Proceedings of the Twentieth Annual ACM-SIAM Symposium on Discrete Algorithms

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It has long been known that for the paging problem in its standard form, competitive analysis cannot adequately distinguish algorithms based on their performance: there exists a vast class of algorithms which achieve the same competitive ratio, ranging from extremely naive and inefficient strategies (such as Flush-When-Full), to strategies of excellent performance in practice (such as Least-Recently-Used and some of its variants). A similar situation arises in the list update problem: in particular, under the cost formulation studied by Martínez and Roura [TCS 2000] and Munro [ESA 2000] every list update algorithm has, asymptotically, the same competitive ratio. Several refinements of competitive analysis, as well as alternative performance measures have been introduced in the literature, with varying degrees of success in narrowing this disconnect between theoretical analysis and empirical evaluation.In this paper we study these two fundamental online problems under the framework of bijective analysis López-Ortiz, SODA 2007 and LATIN 2008]. This is an intuitive technique which is based on pairwise comparison of the costs incurred by two algorithms on sets of request sequences of the same size. Coupled with a well-established model of locality of reference due to Albers, Favrholdt and Giel [JCSS 2005], we show that LeastRecently-Used and Move-to-Front are the unique optimal algorithms for paging and list update, respectively. Prior to this work, only measures based on average-cost analysis have separated LRU and MTF from all other algorithms. Given that bijective analysis is a fairly stringent measure (and also subsumes average-cost analysis), we prove that in a strong sense LRU and MTF stand out as the best algorithms.

show abstract

Probabilistic Analysis of Online Bin Coloring Algorithms Via Stochastic Comparison

Cited by 9 publications

References 24 publications

Comparing online algorithms for bin packing problems

Comparing online algorithms for bin packing problems

Paging and list update under bijective analysis

Paging and List Update under Bijective Analysis

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