The relative worst-order ratio applied to paging

Boyar, Joan; Favrholdt, Lene M.; Larsen, Kim S.

doi:10.1016/j.jcss.2007.03.001

Cited by 44 publications

(70 citation statements)

References 35 publications

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“…Similar results have been presented previously for the paging problem-LRU vs. FWF and look-ahead vs. no look-ahead. See [6] for these results under Relative Worst Order Analysis and [1] for Bijective Analysis.…”

Section: Discussionmentioning

confidence: 99%

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A Comparison of Performance Measures for Online Algorithms

Boyar

Irani

Larsen

2009

Lecture Notes in Computer Science

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Abstract. This paper provides a systematic study of several proposed measures for online algorithms in the context of a specific problem, namely, the two server problem on three colinear points. Even though the problem is simple, it encapsulates a core challenge in online algorithms which is to balance greediness and adaptability. We examine Competitive Analysis, the Max/Max Ratio, the Random Order Ratio, Bijective Analysis and Relative Worst Order Analysis, and determine how these measures compare the Greedy Algorithm and Lazy Double Coverage, commonly studied algorithms in the context of server problems. We find that by the Max/Max Ratio and Bijective Analysis, Greedy is the better algorithm. Under the other measures, Lazy Double Coverage is better, though Relative Worst Order Analysis indicates that Greedy is sometimes better. Our results also provide the first proof of optimality of an algorithm under Relative Worst Order Analysis.

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Section: Discussionmentioning

confidence: 99%

“…Relative Worst Order Analysis: Relative Worst Order Analysis was introduced in [5] and extended in [6]. It compares two online algorithms directly.…”

Section: Quality Measuresmentioning

confidence: 99%

A Comparison of Performance Measures for Online Algorithms

Boyar

Irani

Larsen

2009

Lecture Notes in Computer Science

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“…Relative Worst Order Analysis was introduced in [6] and extended in [7]. It compares two online algorithms directly.…”

Section: Relative Worst Order Analysismentioning

confidence: 99%

A Comparison of Performance Measures for Online Algorithms

2014

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This paper provides a systematic study of several proposed measures for online algorithms in the context of a specific problem, namely, the two server problem on three colinear points. Even though the problem is simple, it encapsulates a core challenge in online algorithms which is to balance greediness and adaptability. We examine Competitive Analysis, the Max/Max Ratio, the Random Order Ratio, Bijective Analysis and Relative Worst Order Analysis, and determine how these measures compare the Greedy Algorithm, Double Coverage, and Lazy Double Coverage, commonly studied algorithms in the context of server problems. We find that by the Max/Max Ratio and Bijective Analysis, Greedy is the best of the three algorithms. Under the other measures, Double Coverage and Lazy Double Coverage are better, though Relative Worst Order Analysis indicates that Greedy is sometimes better. Only Bijective Analysis and Relative Worst Order Analysis indicate that Lazy Double Coverage is better than Double Coverage. Our results also provide the first proof of optimality of an algorithm under Relative Worst Order Analysis.

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“…The discrepancy between theoretical analysis and empirical performance was observed as early as in [35] and spawned an extensive line of research on refined definitions of the competitive ratio as well as on alternative measures for the analysis of online algorithms in general, and for the paging problem in particular. Among the known approaches are: the Max-Max ratio of Ben-David and Borodin [9]; the diffuse adversary model of Koutsoupias and Papadimitriou [28] and Young [39] [40]; loose competitiveness of Young [38] [41]; the random order ratio of Kenyon [27]; the relative worst-order ratio of Boyar, Favrholdt and Larsen [14] and Boyar, Ehmsen and Larsen [13]; and the accommodation function model of Boyar, Larsen and Nielsen [16]. Temporal locality of reference permeates memory access in computer systems, and is a wellestablished property of a typical request sequence in paging.…”

Section: Preliminaries and Related Workmentioning

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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The relative worst-order ratio applied to paging

Cited by 44 publications

References 35 publications

A Comparison of Performance Measures for Online Algorithms

A Comparison of Performance Measures for Online Algorithms

A Comparison of Performance Measures for Online Algorithms

Paging and list update under bijective analysis

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