We study integrated prefetching and caching problems following the work of Cao et. al. [3] and Kimbrel and Karlin [14]. Cao et. al. and Kimbrel and Karlin gave approximation algorithms for minimizing the total elapsed time in single and parallel disk settings. The total elapsed time is the sum of the processor stall times and the length of the request sequence to be served. We show that an optimum prefetching/caching schedule for a single disk problem can be computed in polynomial time, thereby settling an open question by Kimbrel and Karlin. For the parallel disk problem we give an approximation algorithm for minimizing stall time. Stall time is an important and harder to approximate measure for this problem. All of our algorithms are based on a new approach which involves formulating the prefetching/caching problems as integer programs.

In this paper we devise new paging heuristics motivated by the access graph model of paging [2]. Unlike the access graph model [2, 9, 4] and the related Markov paging model [11] our heuristics are truly online in that we do not assume any prior knowledge of the program just about to be executed. The Least Recently Used heuristic for paging is remarkably good, and is known experimentally to be superior to many of the suggested alternatives on real program traces [24]. Experiments we've performed suggest that our heuristics beat LRU consistently, over a wide range of cache sizes and programs. The number of page faults can be as low as 75% less than the number of page faults for LRU and is typically 5%--30% less than that of LRU. We have built a program tracer that gives the page access sequence for real program executions of 200 -- 1,500 thousand page access requests, and our simulations are based on these real program traces. While we have no real evidence to suggest that the programs...

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 worst-case 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 worst-case 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

Caching (paging) is a well-studied problem in online algorithms, usually studied under the assumption that all pages have a uniform size and a uniform fault cost (uni- form caching). However, recent applications related to the web involve situations in which pages can be of different sizes and costs. This general caching problem seems more intricate than the uniform version. In particular, the offline case itself is NP-hard. Only a few results exist for the general caching problem [8, 17]. This paper seeks to develop good offline page replacement policies for the general caching problem, with the hope that any insight gained here may lead to good online algorithms. Our first main result is that by using only a small amount of additional memory, say O(1) times the largest page size, we can obtain an O(1)-approximation to the general caching problem. Note that the largest page size is typically a very small fraction of the total cache size, say 1%. Our second result is that when no add...

This chapter presents an introduction to the competitive analysis of online algorithms. In an online problem...

Paging (caching) is the problem of managing a twolevel memory hierarchy in order to minimize the time required to process a sequence of memory accesses. In order to measure this quantity, we define the system parameter miss penalty to represent the extra time required to access slow memory. In the context of paging, miss penalty is large, so most previous studies of on-line paging have implicitly set miss penalty = 1 in order to simplify the model. We show that this seemingly insignificant simplification substantially alters the precision of derived results. Consequently, we reintroduce miss penalty to the paging problem and present a more accurate analysis of on-line paging (and caching). We validate using this more accurate model by deriving intuitively appealing results for the paging problem which cannot be derived using the simplified model. 1 Introduction Over the past decade, competitive analysis has been extensively used to analyze the performance of paging 1 algorithms [20...

In the paging problem we have to manage a two-level memory system, in which the first level has short access time but can hold only up to k pages, while the second level is very large but slow. We use competitive analysis to study the relative performance of the two best known algorithms for paging, LRU and FIFO. Sleator and Tarjan proved that the competitive ratio of LRU and FIFO is k. In practice, however, LRU is known to perform much better than FIFO. It is believed that the superiority of LRU can be attributed to locality of reference exhibited in request sequences. In order to study this phenomenon, Borodin, Irani, Raghavan and Schieber [2] refined the competitive approach by introducing the concept of access graphs. They conjectured that the competitive ratio of LRU on each access graph is less than or equal to the competitive ratio of FIFO. We prove this conjecture in this paper. 1 Introduction. In the paging problem we have a two-level memory system, in which the first level i...

Consider a finite list of items n = 1; 2; : : : ; N , that are requested according to an i.i.d. process. Each time an item is requested it is moved to the front of the list. The associated search cost C N for accessing an item is equal to its position before being moved. If the request distribution converges to a proper distribution as N ! 1, then the stationary search cost C N converges in distribution to a limiting search cost C. We show that, when the (limiting) request distribution has a heavy tail (e.g., generalized Zipf's law) P[R = n] ¸ c=n ff as n !1, ff ? 1, then the limiting stationary search cost distribution P[C ? n], or, equivalently, the Least-Recently-Used (LRU) caching fault probability, satisfies lim n!1 P[C ? n] P[R ? n] = ` 1 \Gamma 1 ff ' \Gamma ` 1 \Gamma 1 ff ' ff % e fl as ff !1; where \Gamma is the Gamma function and fl (= 0:5772 : : : ) is Euler's constant. When the request distribution has a light tail P[R = n] ¸ ce \Gamman fi as...

This paper gives a randomized competitive distributed paging algorithm called Heat & Dump. The competitive ratio is logarithmic in the total storage capacity of the network, this is optimal to within a constant factor. This is in contrast to the linear optimal deterministic competitive ratio [BFR92]. 1 Introduction The basic paradigm: Distributed Virtual Memory. Virtual addressing has the advantage that the physical address is separate from the logical address [KELS62]. Briefly, the name of a memory item is decoupled from its physical location in memory; moreover, physical location may dynamically change in the run-time. With the appearance of the massively parallel machines in the 1980s, it was natural to extend the virtual memory concept from the traditional uni-processor to distributed shared-memory environment. In other words, the programmer can use the convenient Parallel Random Access Machine (PRAM) abstraction to write the program, which will be then compiled automatically ...

Andrew Chou Jeremy Cooperstock y Ran El--Yaniv z Michael Klugerman x Tom Leighton -- November, 1993 Abstract The distributional approach and competitive analysis have traditionally been used for the design and analysis of on-line algorithms. The former assumes a specific distribution on inputs, while the latter assumes inputs are chosen by an unrestricted adversary. This paper employs the statistical adversary (recently proposed by Raghavan) to analyze and design on-line algorithms for two-way currency trading. The statistical adversary approach may be viewed as a hybrid of the distributional approach and competitive analysis. By statistical adversary, we mean an adversary that generates input sequences, where each sequence must satisfy certain general statistical properties. The on-line algorithms presented in this paper have some very attractive properties. For instance, the algorithms are money-making; they are guaranteed to be profitable when the optimal off-li...