On the competitiveness of the move-to-front rule

Martínez, Conrado; Roura, Salvador

doi:10.1016/s0304-3975(98)00264-3

Cited by 14 publications

(18 citation statements)

References 20 publications

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“…Martínez and Roura [29] and Munro [30] observed that in a realistic setting, rearranging the first i items of the list according to a permutation of {1, . .…”

Section: Preliminaries and Related Workmentioning

confidence: 99%

“…In subsequent work, Martínez and Roura [29] and Munro [30] independently argued that the standard-cost model penalizes reasonable algorithms which in practice can be quite efficient. Instead, they proposed a different cost formulation (to which, following [5] we refer as the modified-cost model) and showed that every online algorithm has asymptotically the same, non-constant competitive ratio, namely Θ(l/log l), where l is the size of the list.…”

Section: Introductionmentioning

confidence: 99%

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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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“…Martínez and Roura [29] and Munro [30] observed that in a realistic setting, rearranging the first i items of the list according to a permutation of {1, . .…”

Section: Preliminaries and Related Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Paging and list update under bijective analysis

Angelopoulos

Schweitzer

2013

J. ACM

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show abstract

“…While list update algorithms with better competitive ratio tend to have better performance in practice the validity of the cost model has been debated. More precisely, Martínez and Roura [18] and Munro [19], independently addressed the drawbacks of the standard cost model. Let (a 1 , a 2 , .…”

Section: Introductionmentioning

confidence: 99%

“…Our main result proves that under both the standard and the modified cost functions MTF is never outperformed in our model, while it always outperforms any other on-line list update algorithm in at least one instance. As mentioned earlier, Martínez and Roura [18] posed the open problem of finding an alternative measure that shows the superiority of MTF in the modified cost model and suggested that this can be done by adding some restrictions over the sequences of requests. Our analysis technique allows us to resolve this problem as well.…”

Section: Introductionmentioning

confidence: 99%

List Update with Locality of Reference

Angelopoulos

Dorrigiv

López-Ortíz

Lecture Notes in Computer Science

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“…Some other algorithms, such as the Timestamp algorithm [2] are also 2-competitive in this model. In subsequent work, Martínez and Roura [25] and Munro [26] independently argued that the standard-cost model penalizes reasonable algorithms which in practice can be quite efficient. Instead, they proposed a different cost formulation (to which, following [4] we refer as the modified-cost model) and showed that every online algorithm has asymptotically the same, non-constant competitive ratio, namely Θ(l/log l), where l is the size of the list.…”

Section: Introductionmentioning

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

On the competitiveness of the move-to-front rule

Cited by 14 publications

References 20 publications

Paging and list update under bijective analysis

Paging and list update under bijective analysis

List Update with Locality of Reference

Paging and List Update under Bijective Analysis

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