Randomized competitive algorithms for the list update problem

Reingold, Nick; Westbrook, Jeffery; Sleator, Daniel D.

doi:10.1007/bf01294261

Cited by 80 publications

(58 citation statements)

References 17 publications

(16 reference statements)

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“…BIT is the randomized algorithm which, for each item in the list, initially chooses randomly and independently with probability 1/2 whether that item should be moved to the front on odd or even accesses to it. BIT is 1.75-competitive [27]. COMB achieves a competitive ratio of 1.6, so for any request sequence I, either Timestamp must achieve a performance ratio of 1.6 compared to Opt, or there must be some setting of the randomized bits for BIT which achieves a ratio of 1.6.…”

Section: Cost Formentioning

confidence: 99%

On the List Update Problem with Advice

Boyar

Kamali

Larsen

et al. 2014

Language and Automata Theory and Applications

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We study the online list update problem under the advice model of computation. Under this model, an online algorithm receives partial information about the unknown parts of the input in the form of some bits of advice generated by a benevolent offline oracle. We show that advice of linear size is required and sufficient for a deterministic algorithm to achieve an optimal solution or even a competitive ratio better than 15/14. On the other hand, we show that surprisingly two bits of advice are sufficient to break the lower bound of 2 on the competitive ratio of deterministic online algorithms and achieve a deterministic algorithm with a competitive ratio of 1.6. In this upper-bound argument, the bits of advice determine the algorithm with smaller cost among three classical online algorithms, Timestamp and two members of the Mtf2 family of algorithms. We also show that Mtf2 algorithms are 2.5-competitive.

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Section: Cost Formentioning

confidence: 99%

On the List Update Problem with Advice

Boyar

Kamali

Larsen

et al. 2014

Language and Automata Theory and Applications

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“…It is possible to measure the amount of random bits needed by a randomized algorithm as a function of the input length, in a similar way as the time complexity, space complexity, or advice complexity is measured. Randomized algorithms that use only constant number of random bits, regardless of the input size, are called barely random algorithms [2], introduced in [11]. The number of random bits used by these algorithms is asymptotically minimal, hence they can be considered the best algorithms with respect to the amount of randomness used.…”

Section: Definitionmentioning

confidence: 99%

Advice Complexity and Barely Random Algorithms

Komm

Královič

2011

SOFSEM 2011: Theory and Practice of Computer Science

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Abstract. Recently, a new measurement -the advice complexity -was introduced for measuring the information content of online problems. The aim is to measure the bitwise information that online algorithms lack, causing them to perform worse than offline algorithms. Among a large number of problems, a well-known scheduling problem, job shop scheduling with unit length tasks, and the paging problem were analyzed within this model. We observe some connections between advice complexity and randomization. Our special focus goes to barely random algorithms, i. e., randomized algorithms that use only a constant number of random bits, regardless of the input size. We apply the results on advice complexity to obtain efficient barely random algorithms for both the job shop scheduling and the paging problem. Furthermore, so far, it has not yet been investigated for job shop scheduling how good an online algorithm may perform when only using a very small (e. g., constant) number of advice bits. In this paper, we answer this question by giving both lower and upper bounds, and also improve the best known upper bound for optimal algorithms.

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“…Finally, we mention other somewhat related work in the realm of online computation: see the work of Karlin et al [15] for ski-rental problems, Reingold et al [16] for list access problems, and Fiat et al [17] for paging.…”

Section: Introductionmentioning

confidence: 99%