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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...
Asymptotic approximation of the movetofront search cost distribution and leastrecentlyused caching fault probabilities
, 1999
"... 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 distribu ..."
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Cited by 23 (8 self)
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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 → ∞, 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 α as n → ∞, α> 1, then the limiting stationary search cost distribution P�C> n�, or, equivalently, the leastrecently used (LRU) caching fault probability, satisfies P�C> n� lim n→ ∞ P�R> n � =
SelfOrganizing Data Structures
 In
, 1998
"... . We survey results on selforganizing data structures for the search problem and concentrate on two very popular structures: the unsorted linear list, and the binary search tree. For the problem of maintaining unsorted lists, also known as the list update problem, we present results on the competit ..."
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Cited by 18 (0 self)
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. We survey results on selforganizing data structures for the search problem and concentrate on two very popular structures: the unsorted linear list, and the binary search tree. For the problem of maintaining unsorted lists, also known as the list update problem, we present results on the competitiveness achieved by deterministic and randomized online algorithms. For binary search trees, we present results for both online and offline algorithms. Selforganizing data structures can be used to build very effective data compression schemes. We summarize theoretical and experimental results. 1 Introduction This paper surveys results in the design and analysis of selforganizing data structures for the search problem. The general search problem in pointer data structures can be phrased as follows. The elements of a set are stored in a collection of nodes. Each node also contains O(1) pointers to other nodes and additional state data which can be used for navigation and selforganizati...
Offline Algorithms for The List Update Problem
, 1996
"... Optimum offline algorithms for the list update problem are investigated. The list update problem involves implementing a dictionary of items as a linear list. Several characterizations of optimum algorithms are given; these lead to optimum algorithm which runs in time \Theta2 n (n \Gamma 1)!m, wh ..."
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Cited by 14 (2 self)
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Optimum offline algorithms for the list update problem are investigated. The list update problem involves implementing a dictionary of items as a linear list. Several characterizations of optimum algorithms are given; these lead to optimum algorithm which runs in time \Theta2 n (n \Gamma 1)!m, where n is the length of the list and m is the number of requests. The previous best algorithm, an adaptation of a more general algorithm due to Manasse et al. [9], runs in time \Theta(n!) 2 m. 1 Introduction A dictionary is an abstract data type that stores a collection of keyed items and supports the operations access, insert, and delete. In the sequential search or list update problem, a dictionary is implemented as simple linear list, either stored as a linked collection of items or as an array. An access is done by starting at the front of the list and examining each succeeding item until either finding the item desired or reaching the end of the list and reporting the item not present...
A competitive analysis of the list update problem with lookahead
 Theoret. Comput. Sci
, 1998
"... We consider the question of lookahead in the list update problem: What improvement can be achieved in terms of competitiveness if an online algorithm sees not only the present request to be served but also some future requests? We introduce two different models of lookahead and study the list updat ..."
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Cited by 13 (0 self)
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We consider the question of lookahead in the list update problem: What improvement can be achieved in terms of competitiveness if an online algorithm sees not only the present request to be served but also some future requests? We introduce two different models of lookahead and study the list update problem using these models. We develop lower bounds on the competitiveness that can be achieved by deterministic online algorithms with lookahead. Furthermore we present online algorithms with lookahead that are competitive against static offline algorithms.
LeastRecentlyUsed Caching with Dependent Requests
 Theoretical Computer Science
, 2002
"... We investigate a widely popular LeastRecentlyUsed (LRU) cache replacement algorithm with semiMarkov modulated requests. SemiMarkov processes provide the flexibility for modeling strong statistical correlation, including the widely reported longrange dependence in the World Wide Web page request ..."
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Cited by 13 (6 self)
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We investigate a widely popular LeastRecentlyUsed (LRU) cache replacement algorithm with semiMarkov modulated requests. SemiMarkov processes provide the flexibility for modeling strong statistical correlation, including the widely reported longrange dependence in the World Wide Web page request patterns. When the frequency of requesting a page n is equal to the generalized Zipf’s law c/n α,α> 1, our main result shows that the cache fault probability is asymptotically, for large cache sizes, the same as in the corresponding LRU system with i.i.d. requests. The result is asymptotically explicit and appears to be the first computationally tractable averagecase analysis of LRU caching with statistically dependent request sequences. The surprising insensitivity of LRU caching performance demonstrates its robustness to changes in document popularity. Furthermore, we show that the derived asymptotic result and simulation experiments are in excellent agreement, even for relatively small cache sizes. Keywords: leastrecentlyused caching, movetofront, Zipf’s law, heavytailed distributions, longrange dependence, semiMarkov processes, averagecase analysis
Performance of the MoveToFront Algorithm with MarkovModulated Request Sequences
 Operations Research Letters
, 1999
"... We study the classical movetofront (MTF) algorithm for selforganizing lists within the Markovmodulated request (MMR) model. Such models are useful when list accesses are generated within a relatively small set of modes, with the request sequences in each mode being i.i.d.. These modes are often ..."
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Cited by 8 (2 self)
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We study the classical movetofront (MTF) algorithm for selforganizing lists within the Markovmodulated request (MMR) model. Such models are useful when list accesses are generated within a relatively small set of modes, with the request sequences in each mode being i.i.d.. These modes are often called localities of reference and are known to exist in such applications as traffic streams of Ethernet or ATM networks and the locus of control or data accesses of executing computer programs. Our main results are explicit formulas for the mean and variance of the searchcost, the number of accesses required to find a given list element. By adjusting the number of modes, one can use the MMR methodology to trade off the quality of an approximation with the computational effort it requires. Thus, our results provide a useful new tool for evaluating the MTF rule in linearsearch applications with correlated request sequences. We illustrate the computations with several examples. Keywords: Se...
Selforganizing data structures with dependent accesses
 ICALP'96, LNCS 1099
, 1995
"... We consider selforganizing data structures in the case where the sequence of accesses can be modeled by a first order Markov chain. For the simplek and batchedkmovetofront schemes, explicit formulae for the expected search costs are derived and compared. We use a new approach that employs th ..."
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Cited by 5 (1 self)
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We consider selforganizing data structures in the case where the sequence of accesses can be modeled by a first order Markov chain. For the simplek and batchedkmovetofront schemes, explicit formulae for the expected search costs are derived and compared. We use a new approach that employs the technique of expanding a Markov chain. This approach generalizes the results of Gonnet/Munro/Suwanda. In order to analyze arbitrary memoryfree moveforward heuristics for linear lists, we restrict our attention to a special access sequence, thereby reducing the state space of the chain governing the behaviour of the data structure. In the case of accesses with locality (inert transition behaviour), we find that the hierarchies of selforganizing data structures with respect to the expected search time are reversed, compared with independent accesses. Finally we look at selforganizing binary trees with the movetoroot rule and compare the expected search cost with the entropy of the Markov chain of accesses.
A Probabilistic Defense Mechanism Against Distributed Denial of Service Attacks
"... Distributed denial of service attacks form a prolific threat to any form of clientserver computing, as used, for instance, by ecommerce businesses. The resources of standard servers are quickly consumed under such an attack, making them unavailable to legitimate users. We describe and analyze a ..."
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Cited by 2 (0 self)
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Distributed denial of service attacks form a prolific threat to any form of clientserver computing, as used, for instance, by ecommerce businesses. The resources of standard servers are quickly consumed under such an attack, making them unavailable to legitimate users. We describe and analyze a defense mechanism for such servers. We prove that this mechanism favors benign users, making the server less volatile to such attacks.
Analysis of TTLbased Cache Networks
"... Many researchers have been working on the performance analysis of caching in InformationCentric Networks (ICNs) under various replacement policies like Least Recently Used (LRU), FIFO or Random (RND). However, no exact results are provided, and many approximate models do not scale even for the simp ..."
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Cited by 1 (0 self)
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Many researchers have been working on the performance analysis of caching in InformationCentric Networks (ICNs) under various replacement policies like Least Recently Used (LRU), FIFO or Random (RND). However, no exact results are provided, and many approximate models do not scale even for the simple network of two caches connected in tandem. In this paper, we introduce a TimeToLive based policy (TTL), that assigns a timer to each content stored in the cache and redraws the timer each time the content is requested (at each hit/miss). We show that our TTL policy is more general than LRU, FIFO or RND, since it is able to mimic their behavior under an appropriate choice of its parameters. Moreover, the analysis of networks of TTLbased caches appears simpler not only under the Independent Reference Model (IRM, on which many existing results rely) but also with the Renewal Model for requests. In particular, we determine exact formulas for the performance metrics of interest for a linear network and a tree network with one root cache and N leaf caches. For more general networks, we propose an approximate solution with the relative errors smaller than 10 −3 and 10 −2 for exponentially distributed and constant TTLs respectively. 1.