Competitive snoopy caching

Karlin, Anna R.; Manasse, Mark S.; Rudolph, Larry; Sleator, Daniel D.

doi:10.1007/bf01762111

Cited by 550 publications

(325 citation statements)

References 8 publications

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“…Consider the representation of r (k) , (21). It is clear that r (k) < M/m since the competitive ratio M/m is attained by the trivial strategy that trades all dollars in the minimum possible rate, m, and the threat-based algorithm certainly performs strictly better.…”

Section: Proof As Usual Suppose Thatmentioning

confidence: 99%

Optimal Search and One-Way Trading Online Algorithms

et al. 2001

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Abstract. This paper is concerned with the time series search and one-way trading problems. In the (time series) search problem a player is searching for the maximum (or minimum) price in a sequence that unfolds sequentially, one price at a time. Once during this game the player can decide to accept the current price p in which case the game ends and the player's payoff is p. In the one-way trading problem a trader is given the task of trading dollars to yen. Each day, a new exchange rate is announced and the trader must decide how many dollars to convert to yen according to the current rate. The game ends when the trader trades his entire dollar wealth to yen and his payoff is the number of yen acquired.The search and one-way trading are intimately related. Any (deterministic or randomized) one-way trading algorithm can be viewed as a randomized search algorithm. Using the competitive ratio as a performance measure we determine the optimal competitive performance for several variants of these problems. In particular, we show that a simple threat-based strategy is optimal and we determine its competitive ratio which yields, for realistic values of the problem parameters, surprisingly low competitive ratios.We also consider and analyze a one-way trading game played against an adversary called Nature where the online player knows the probability distribution of the maximum exchange rate and that distribution has been chosen by Nature. Finally, we consider some applications for a special case of portfolio selection called two-way trading in which the trader may trade back and forth between cash and one asset.

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Section: Proof As Usual Suppose Thatmentioning

confidence: 99%

Optimal Search and One-Way Trading Online Algorithms

et al. 2001

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“…Such a modeling corresponds to non-marking algorithms, as it does not allow the algorithm to use information beyond the set of pages that are currently in the cache. In the course of applying our implementation of the symbolic algorithm to paging, we have realized that the only nonmarking competitive algorithm for paging we are aware of, Flush-when-Full (FWF) [BEY98,KMRS88], is not lazy (also referred to as "demand paging" in [BEY98]); that is, it may evict from the cache more than a single page in case an eviction is required. From a practical standpoint, such evictions are wasteful, and a reasonable implementation of FWF would keep the cache full at all times and only mark the pages spuriously evicted by FWF -thus treating FWF as a marking algorithm.…”

Section: Symbolic Model-checking Algorithmmentioning

confidence: 99%

Formal Analysis of Online Algorithms

Aminof

Kupferman

Lampert

2011

Automated Technology for Verification and Analysis

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Abstract. In [AKL10], we showed how viewing online algorithms as reactive systems enables the application of ideas from formal verification to the competitive analysis of online algorithms. Our approach is based on weighted automata, which assign to each input word a cost in IR ≥0 . By relating the "unbounded look ahead" of optimal offline algorithms with nondeterminism, and relating the "no look ahead" of online algorithms with determinism, we were able to solve problems about the competitive ratio of online algorithms and the memory they require. In this paper we improve the application in three important and technically challenging aspects. First, we allow the competitive analysis to take into account assumptions about the environment. Second, we allow the online algorithm to have a bounded lookahead. Third, we describe a symbolic version of the model-checking algorithm and demonstrate its applicability. The first two contributions broaden the scope of our approach to settings in which the traditional analysis of online algorithms is particularly complicated. The third contribution improves the practicality of our approach and enables it to handle larger state spaces.

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“…The data stream model appears to be related to other work e.g., on competitive analysis [69], or I/O efficient algorithms [98]. However, it is more restricted in that it requires that a data item can never again be retrieved in main memory after its first pass (if it is a one-pass algorithm).…”

Section: The Data Stream Computation Modelmentioning

confidence: 99%