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24
Optimal Prefetching via Data Compression
, 1995
"... Caching and prefetching are important mechanisms for speeding up access time to data on secondary storage. Recent work in competitive online algorithms has uncovered several promising new algorithms for caching. In this paper we apply a form of the competitive philosophy for the first time to the pr ..."
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Cited by 238 (10 self)
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Caching and prefetching are important mechanisms for speeding up access time to data on secondary storage. Recent work in competitive online algorithms has uncovered several promising new algorithms for caching. In this paper we apply a form of the competitive philosophy for the first time to the problem of prefetching to develop an optimal universal prefetcher in terms of fault ratio, with particular applications to largescale databases and hypertext systems. Our prediction algorithms for prefetching are novel in that they are based on data compression techniques that are both theoretically optimal and good in practice. Intuitively, in order to compress data effectively, you have to be able to predict future data well, and thus good data compressors should be able to predict well for purposes of prefetching. We show for powerful models such as Markov sources and nth order Markov sources that the page fault rates incurred by our prefetching algorithms are optimal in the limit for almost all sequences of page requests.
Competitive Paging With Locality of Reference
 Journal of Computer and System Sciences
, 1991
"... Abstract The SleatorTarjan competitive analysis of paging [Comm. of the ACM; 28:202 208, 1985] gives us the ability to make strong theoretical statements about the performance of paging algorithms without making probabilistic assumptions on the input. Nevertheless practitioners voice reservations ..."
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Cited by 120 (3 self)
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Abstract The SleatorTarjan competitive analysis of paging [Comm. of the ACM; 28:202 208, 1985] gives us the ability to make strong theoretical statements about the performance of paging algorithms without making probabilistic assumptions on the input. Nevertheless practitioners voice reservations about the model, citing its inability to discern between LRU and FIFO (algorithms whose performances differ markedly in practice), and the fact that the theoretical competitiveness of LRU is much larger than observed in practice. In addition, we would like to address the following important question: given some knowledge of a program's reference pattern, can we use it to improve paging performance on that program?
MARKOV PAGING
, 2000
"... This paper considers the problemof paging under the assumption that the sequence of pages accessed is generated by a Markov chain. We use this model to study the faultrate of paging algorithms. We first draw on the theory of Markov decision processes to characterize the paging algorithmthat achieve ..."
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Cited by 60 (4 self)
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This paper considers the problemof paging under the assumption that the sequence of pages accessed is generated by a Markov chain. We use this model to study the faultrate of paging algorithms. We first draw on the theory of Markov decision processes to characterize the paging algorithmthat achieves optimal faultrate on any Markov chain. Next, we address the problemof devising a paging strategy with low faultrate for a given Markov chain. We show that a number of intuitive approaches fail. Our main result is a polynomialtime procedure that, on any Markov chain, will give a paging algorithm with faultrate at most a constant times optimal. Our techniques show also that some algorithms that do poorly in practice fail in the Markov setting, despite known (good) performance guarantees when the requests are generated independently from a probability distribution.
Randomized Competitive Algorithms for the List Update Problem
 Algorithmica
, 1992
"... We prove upper and lower bounds on the competitiveness of randomized algorithms for the list update problem of Sleator and Tarjan. We give a simple and elegant randomized algorithm that is more competitive than the best previous randomized algorithm due to Irani. Our algorithm uses randomness only d ..."
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Cited by 39 (2 self)
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We prove upper and lower bounds on the competitiveness of randomized algorithms for the list update problem of Sleator and Tarjan. We give a simple and elegant randomized algorithm that is more competitive than the best previous randomized algorithm due to Irani. Our algorithm uses randomness only during an initialization phase, and from then on runs completely deterministically. It is the first randomized competitive algorithm with this property to beat the deterministic lower bound. We generalize our approach to a model in which access costs are fixed but update costs are scaled by an arbitrary constant d. We prove lower bounds for deterministic list update algorithms and for randomized algorithms against oblivious and adaptive online adversaries. In particular, we show that for this problem adaptive online and adaptive offline adversaries are equally powerful. 1 Introduction Recently much attention has been given to competitive analysis of online algorithms [7, 20, 22, 25]. Ro...
Optimal Prediction for Prefetching in the Worst Case
, 1998
"... Response time delays caused by I/O are a major problem in many systems and database applications. Prefetching and cache replacement methods are attracting renewed attention because of their success in avoiding costly I/Os. Prefetching can be looked upon as a type of online sequential prediction, whe ..."
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Cited by 27 (7 self)
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Response time delays caused by I/O are a major problem in many systems and database applications. Prefetching and cache replacement methods are attracting renewed attention because of their success in avoiding costly I/Os. Prefetching can be looked upon as a type of online sequential prediction, where the predictions must be accurate as well as made in a computationally efficient way. Unlike other online problems, prefetching cannot admit a competitive analysis, since the optimal offline prefetcher incurs no cost when it knows the future page requests. Previous analytical work on prefetching [J. Assoc. Comput. Mach., 143 (1996), pp. 771–793] consisted of modeling the user as a probabilistic Markov source. In this paper, we look at the much stronger form of worstcase analysis and derive a randomized algorithm for pure prefetching. We compare our algorithm for every page request sequence with the important class of finite state prefetchers, making no assumptions as to how the sequence of page requests is generated. We prove analytically that the fault rate of our online prefetching algorithm converges almost surely for every page request sequence to the fault rate of the optimal finite state prefetcher for the sequence. This analysis model can be looked upon as a generalization of the competitive framework, in that it compares an online algorithm in a worstcase manner over all sequences with a powerful yet nonclairvoyant opponent. We simultaneously achieve the computational goal of implementing our prefetcher in optimal constant expected time per prefetched page using the optimal dynamic discrete random variate generator of Matias, Vitter, and Ni [Proc. 4th Annual SIAM/ACM
A Theoretical Framework for MemoryAdaptive Algorithms
 In IEEE Symposium on Foundations of Computer Science
, 1999
"... External Memory algorithms play a key role in database management systems and large scale processing systems. External memory algorithms are typically tuned for efficient performance given a fixed, statically allocated amount of internal memory. However, with the advent of realtime database system ..."
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Cited by 15 (0 self)
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External Memory algorithms play a key role in database management systems and large scale processing systems. External memory algorithms are typically tuned for efficient performance given a fixed, statically allocated amount of internal memory. However, with the advent of realtime database system and database systems based upon administratively defined goals, algorithms must increasingly be able to adapt in an online manner when the amount of internal memory allocated to them changes dynamically and unpredictably. In this paper, we present a theoretical and applicable framework for memoryadaptive algorithms (or simply MA algorithms). We define the competitive worstcase notion of what it means for an MA algorithm to be dynamically optimal and prove fundamental lower bounds on the performance of MA algorithms for problems such as sorting, standard matrix multiplication, and several related problems. Our main tool for proving dynamic optimality is the notion of resource consumption, wh...
Page Migration Algorithms Using Work Functions
 In Proc. of the 4th Int. Symp. on Algorithms and Computation (ISAAC
, 1994
"... The page migration problem occurs in managing a globally addressed shared memory in a multiprocessor system. Each physical page of memory is located at a given processor, and memory references to that page by other processors are charged a cost equal to the network distance. At times the page may mi ..."
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Cited by 13 (1 self)
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The page migration problem occurs in managing a globally addressed shared memory in a multiprocessor system. Each physical page of memory is located at a given processor, and memory references to that page by other processors are charged a cost equal to the network distance. At times the page may migrate between processors, at a cost equal to the distance times a page size factor, D. The problem is to schedule movements online so as to minimize the total cost of memory references. Page migration can also be viewed as a restriction of the 1server with excursions problem. This paper presents a collection of algorithms and lower bounds for the page migration problem in various settings. Competitive analysis is used. The competitiveness of an online algorithm is the worstcase ratio of its cost to the optimum cost on any sequence of requests. Randomized (2 + 1 2D )competitive online algorithms are given for trees and products of trees, including the mesh and the hypercube, and for un...
ApplicationControlled Paging for a Shared Cache
 Proc. of FOCS'95
, 1995
"... We propose a provably efficient applicationcontrolled global strategy for organizing a cache of size k shared among P application processes. Each application has access to information about its own future page requests, and by using that local information along with randomization in the context of ..."
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Cited by 8 (0 self)
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We propose a provably efficient applicationcontrolled global strategy for organizing a cache of size k shared among P application processes. Each application has access to information about its own future page requests, and by using that local information along with randomization in the context of a global caching algorithm, we are able to break through the conventional H k ln k lower bound on the competitive ratio for the caching problem. If the P application processes always make good cache replacement decisions, our online applicationcontrolled caching algorithm attains a competitive ratio of 2HP \Gamma1 + 2 2 ln P . Typically, P is much smaller than k, perhaps by several orders of magnitude. Our competitive ratio improves upon the 2P + 2 competitive ratio achieved by the deterministic applicationcontrolled strategy of Cao, Felten, and Li. We show that no online applicationcontrolled algorithm can have a competitive ratio better than minfHP \Gamma1 ; H k g, even if each application process has perfect knowledge of its individual page request sequence. Our results are with respect to a worstcase interleaving of the individual page request sequences of the P application processes.
Can Entropy Characterize Performance of Online Algorithms?
 in Symposium on Discrete Algorithms, 2001
, 2001
"... We focus in this work on an aspect of online computation that is not addressed by the standard competitive analysis. Namely, identifying request sequences for which nontrivial online algorithms are useful versus request sequences for which all algorithms perform equally bad. The motivation for t ..."
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Cited by 6 (1 self)
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We focus in this work on an aspect of online computation that is not addressed by the standard competitive analysis. Namely, identifying request sequences for which nontrivial online algorithms are useful versus request sequences for which all algorithms perform equally bad. The motivation for this work are advanced system and architecture designs which allow the operating system to dynamically allocate resources to online protocols such as prefetching and caching. To utilize these features the operating system needs to identify data streams that can benet from more resources. Our approach in this work is based on the relation between entropy, compression and gambling, extensively studied in information theory. It has been shown that in some settings entropy can either fully or at least partially characterize the expected outcome of an iterative gambling game. Viewing online problem with stochastic input as an iterative gambling game, our goal is to study the extent to which the entropy of the input characterizes the expected performance of online algorithms for problems that arise in computer applications. We study bounds based on entropy for three online problems { list accessing, prefetching and caching. We show that entropy is a good performance characterizer for prefetching, but not so good characterizer for online caching. Our work raises several open questions in using entropy as a predictor in online computation. Computer Science Department, Brown University, Box 1910, Providence, RI 029121910, USA. Email: fgopal, elig@cs.brown.edu. Supported in part by NSF grant CCR9731477. A preliminary version of this paper appeared in the proceedings of the 12th annual ACMSIAM Symposium on Discrete Algorithms (SODA), Washington D.C., 2001. 1