OnlineMin: A Fast Strongly Competitive Randomized Paging Algorithm

Brodal, Gerth Stølting; Moruz, Gabriel; Negoescu, Andrei

doi:10.1007/978-3-642-29116-6_14

Cited by 3 publications

(1 citation statement)

References 11 publications

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“…Note that the lower bound for Equitable applies equally to OnlineMin [20], as OnlineMin has the same expected number of faults as Equitable on all request sequences.…”

Section: Theorem 11 (Smoothness Of Partition and Equitable)mentioning

confidence: 99%

On the Smoothness of Paging Algorithms

Reineke

Salinger

2017

Theory Comput Syst

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We study the smoothness of paging algorithms. How much can the number of page faults increase due to a perturbation of the request sequence? We call a paging algorithm smooth if the maximal increase in page faults is proportional to the number of changes in the request sequence. We also introduce quantitative smoothness notions that measure the smoothness of an algorithm. We derive lower and upper bounds on the smoothness of deterministic and randomized demand-paging and competitive algorithms. Among strongly-competitive deterministic algorithms LRU matches the lower bound, while FIFO matches the upper bound. Well-known randomized algorithms like Partition, Equitable, or Mark are shown not to be smooth. We introduce two new randomized algorithms, called Smoothed-LRU and LRU-Random. Smoothed-LRU allows to sacrifice competitiveness for smoothness, where the trade-off is controlled by a parameter. LRU-Random is at least as competitive as any deterministic algorithm while smoother.

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“…Note that the lower bound for Equitable applies equally to OnlineMin [20], as OnlineMin has the same expected number of faults as Equitable on all request sequences.…”

Section: Theorem 11 (Smoothness Of Partition and Equitable)mentioning

confidence: 99%

On the Smoothness of Paging Algorithms

Reineke

Salinger

2017

Theory Comput Syst

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Engineering Efficient Paging Algorithms

Moruz

Negoescu

Neumann

et al. 2012

Experimental Algorithms

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Improved Space Bounds for Strongly Competitive Randomized Paging Algorithms

Moruz

Negoescu

2013

Automata, Languages, and Programming

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Paging is one of the prominent problems in the field of online algorithms. While in the deterministic setting there exist simple and efficient strongly competitive algorithms, in the randomized setting a tradeoff between competitiveness and memory is still not settled. Bein et al. [4] conjectured that there exist strongly competitive randomized paging algorithms, using o(k) bookmarks, i.e. pages not in cache that the algorithm keeps track of. Also in [4] the first algorithm using O(k) bookmarks (2k more precisely), Equitable2, was introduced, proving in the affirmative a conjecture in [7].We prove tighter bounds for Equitable2, showing that it requires less than k bookmarks, more precisely ≈ 0.62k. We then give a lower bound for Equitable2 showing that it cannot both be strongly competitive and use o(k) bookmarks. Nonetheless, we show that it can trade competitiveness for space. More precisely, if its competitive ratio is allowed to be (H k + t), then it requires k/(1 + t) bookmarks.Our main result proves the conjecture that there exist strongly competitive paging algorithms using o(k) bookmarks. We propose an algorithm, denoted Partition2, which is a variant of the Partition algorithm by McGeoch and Sleator [13]. While classical Partition is unbounded in its space requirements, Partition2 uses Θ(k/ log k) bookmarks. Furthermore, we show that this result is asymptotically tight when the forgiveness steps are deterministic.

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OnlineMin: A Fast Strongly Competitive Randomized Paging Algorithm

Cited by 3 publications

References 11 publications

On the Smoothness of Paging Algorithms

On the Smoothness of Paging Algorithms

Engineering Efficient Paging Algorithms

Improved Space Bounds for Strongly Competitive Randomized Paging Algorithms

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