On paging with locality of reference

Albers, Susanne; Favrholdt, Lene M.; Giel, Oliver

doi:10.1145/509907.509949

Cited by 18 publications

(24 citation statements)

References 18 publications

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“…One exemplary result in beyond worst-case analysis is due to Albers et al [2], for the online paging problem described in the introduction. The key idea is to parameterize page request sequences according to how much locality of reference they exhibit, and then prove parameterized worstcase guarantees.…”

Section: Models Of Typical Instancesmentioning

confidence: 99%

Beyond worst-case analysis

Roughgarden

2019

Commun. ACM

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Comparing different algorithms is hard. For almost any pair of algorithms and measure of algorithm performance-like running time or solution quality-each algorithm will perform better than the other on some inputs. 1 For example, the insertion sort algorithm is faster than merge sort on already-sorted arrays but slower on many other inputs. When two algorithms have incomparable performance, how can we deem one of them "better than" the other?Worst-case analysis is a specific modeling choice in the analysis of algorithms, where the overall performance of an algorithm is summarized by its worst performance on any input of a given size. The "better" algorithm is then the one with superior worst-case performance. Merge sort, with its worst-case asymptotic running time of Θ(n log n) for arrays of length n, is better in this sense than insertion sort, which has a worst-case running time of Θ(n 2 ).While crude, worst-case analysis can be tremendously useful, and it is the dominant paradigm for algorithm analysis in theoretical computer science. A good worst-case guarantee is the bestcase scenario for an algorithm, certifying its general-purpose utility and absolving its users from understanding which inputs are relevant to their applications. Remarkably, for many fundamental computational problems, there are algorithms with excellent worst-case performance guarantees. The lion's share of an undergraduate algorithms course comprises algorithms that run in linear or near-linear time in the worst case.For many problems a bit beyond the scope of an undergraduate course, however, the downside of worst-case analysis rears its ugly head. We next review three classical examples where worstcase analysis gives misleading or useless advice about how to solve a problem; further examples in modern machine learning are described later. These examples motivate the alternatives to worstcase analysis described in the rest of the article. 2The simplex method for linear programming. Perhaps the most famous failure of worstcase analysis concerns linear programming, the problem of optimizing a linear function subject to linear constraints (Figure 1). Dantzig's simplex method is an algorithm from the 1940s that

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Section: Models Of Typical Instancesmentioning

confidence: 99%

Beyond worst-case analysis

Roughgarden

2019

Commun. ACM

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“…In chronological order, the main contributions are the following: online/online ratio [45], statistical adversary [61], loose competitive ratio [65], max/max ratio [9], access graphs (incorporating locality of reference) [13], random-order ratio [53], accommodating ratio [25], extra resource analysis [51], diffuse adversary [54], accommodating function [28], smoothed analysis [63], working set (incorporating locality of reference) [2], relative worst-order analysis [18,21], bijective and average analysis [5], relative interval analysis [37], bijective ratio [6], and online-bounded analysis [16,15].…”

Section: Other Performance Measuresmentioning

confidence: 99%

Relative Worst-Order Analysis: A Survey

Boyar

Favrholdt

Larsen

2018

Adventures Between Lower Bounds and Higher Altitudes

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“…An early approach to this, which at the same time addressed issues of locality of reference, was the access graph model [10], where a graph defines which requests are allowed to follow each other. Another locality of reference approach was taken in [2], limiting the maximum number of different requests allowed within some fixed-sized sliding window. Both of these models were targeted at the paging problem, and the techniques are not meant to be generally applicable to online algorithm analysis.…”

Section: Performance Measuresmentioning

confidence: 99%

“…We show that, for a large class of algorithms for dual bin packing containing First-Fit and Best-Fit, the online-bounded ratio is the same as the competitive ratio on accommodating sequences. To show that this does not hold for all algorithms, we also give an example of a 2 3 -competitive algorithm on accommodating sequences that has an online-bounded ratio of 0.…”

Section: Dual Bin Packingmentioning

confidence: 99%

Online Bounded Analysis

Boyar

Epstein

Favrholdt

et al. 2016

Computer Science – Theory and Applications

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Though competitive analysis is often a very good tool for the analysis of online algorithms, sometimes it does not give any insight and sometimes it gives counter-intuitive results. Much work has gone into exploring other performance measures, in particular targeted at what seems to be the core problem with competitive analysis: the comparison of the performance of an online algorithm is made with respect to a too powerful adversary. We consider a new approach to restricting the power of the adversary, by requiring that when judging a given online algorithm, the optimal offline algorithm must perform at least as well as the online algorithm, not just on the entire final request sequence, but also on any prefix of that sequence. This is limiting the adversary's usual advantage of being able to exploit that it knows the sequence is continuing beyond the current request. Through a collection of online problems, including machine scheduling, bin packing, dual bin packing, and seat reservation, we investigate the significance of this particular offline advantage.

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On paging with locality of reference

Cited by 18 publications

References 18 publications

Beyond worst-case analysis

Beyond worst-case analysis

Relative Worst-Order Analysis: A Survey

Online Bounded Analysis

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