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19
Improved Randomized OnLine Algorithms for the List Update Problem
 PROC. 6TH ANNUAL ACMSIAM SYMPOSIUM ON DISCRETE ALGORITHMS
, 1995
"... The best randomized online algorithms known so far for the list update problem achieve a competitiveness of p 3 1:73. In this paper we present a new family of randomized online algorithms that beat this competitive ratio. Our improved algorithms are called TIMESTAMP algorithms and achieve a com ..."
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Cited by 40 (8 self)
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The best randomized online algorithms known so far for the list update problem achieve a competitiveness of p 3 1:73. In this paper we present a new family of randomized online algorithms that beat this competitive ratio. Our improved algorithms are called TIMESTAMP algorithms and achieve a competitiveness of maxf2 \Gamma p; 1 + p(2 \Gamma p)g, for any real number p 2 [0; 1]. Setting p = (3 \Gamma p 5)=2, we obtain a OEcompetitive algorithm, where OE = (1 + p 5)=2 1:62 is the Golden Ratio. TIMESTAMP algorithms coordinate the movements of items using some information on past requests. We can reduce the required information at the expense of increasing the competitive ratio. We present a very simple version of the TIMESTAMP algorithms that is 1:68competitive. The family of TIMESTAMP algorithms also includes a new deterministic 2competitive online algorithm that is different from the MOVETOFRONT rule.
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...
A Combined BIT and TIMESTAMP Algorithm for the List Update Problem
 INFORMATION PROCESSING LETTERS
, 1995
"... We present a randomized online algorithm for the list update problem which achieves a competitive factor of 1.6, the best known so far. The algorithm makes an initial random choice between two known algorithms that have different worstcase request sequences. The first is the BIT algorithm that ..."
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Cited by 27 (11 self)
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We present a randomized online algorithm for the list update problem which achieves a competitive factor of 1.6, the best known so far. The algorithm makes an initial random choice between two known algorithms that have different worstcase request sequences. The first is the BIT algorithm that, for each item in the list, alternates between moving it to the front of the list and leaving it at its place after it has been requested. The second is a TIMESTAMP algorithm that moves an item in front of less often requested items within the list.
Average Case Analyses of List Update Algorithms, with Applications to Data Compression
 Algorithmica
, 1998
"... We study the performance of the Timestamp (0) (TS(0)) algorithm for selforganizing sequential search on discrete memoryless sources. We demonstrate that TS(0) is better than Movetofront on such sources, and determine performance ratios for TS(0) against the optimal offline and static adversaries ..."
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Cited by 21 (4 self)
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We study the performance of the Timestamp (0) (TS(0)) algorithm for selforganizing sequential search on discrete memoryless sources. We demonstrate that TS(0) is better than Movetofront on such sources, and determine performance ratios for TS(0) against the optimal offline and static adversaries in this situation. Previous work on such sources compared online algorithms only with static adversaries. One practical motivation for our work is the use of the Movetofront heuristic in various compression algorithms. Our theoretical results suggest that in many cases using TS(0) in place of Movetofront in schemes that use the latter should improve compression. Tests using implementations on a standard corpus of test documents demonstrate that TS(0) leads to improved compression.
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.
Competitive Algorithms for Multilevel Caching and Relaxed List Update (Extended Abstract)
 Journal of Algorithms
, 1998
"... ) Marek Chrobak John Noga y Abstract We study the Relaxed List Update Problem (RLUP), in which access requests are made to items stored in a list. The cost to access the jth item x j is c j , where c i c i+1 for all i. After the access, x j can be repeatedly swapped, at no cost, with any ite ..."
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Cited by 7 (0 self)
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) Marek Chrobak John Noga y Abstract We study the Relaxed List Update Problem (RLUP), in which access requests are made to items stored in a list. The cost to access the jth item x j is c j , where c i c i+1 for all i. After the access, x j can be repeatedly swapped, at no cost, with any item that precedes it in the list. This problem was introduced by Aggarwal et al [1] as a model for the management of hierarchical memory that consists of a number of caches of increasing size and access time. They also proved that a version of LRU is Ccompetitive, for some C, for a restricted class of cost functions. (1) We give an efficient offline algorithm that computes the optimal strategy for RLUP. We also show an elegant characterization of work functions for RLUP. (2) We prove that MovetoFront (MTF) is optimally competitive for RLUP with any cost function. An interesting feature of the proof is that it does not involve any estimates on the competitive ratio. (3) We give a lower boun...
Competitive Access Time via Dynamic Storage Rearrangement
, 1995
"... We deal with a natural generalization of one of the seminal problems in the study of online computation, list management [ST85a, IRSW91, Irani91]. We consider a doubly linked list with a pointer pointing to the last item accessed. Our goal, as with list management, is to minimize the total number o ..."
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Cited by 4 (0 self)
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We deal with a natural generalization of one of the seminal problems in the study of online computation, list management [ST85a, IRSW91, Irani91]. We consider a doubly linked list with a pointer pointing to the last item accessed. Our goal, as with list management, is to minimize the total number of pointers traversed over a sequence of searches. This problem models issues of dynamic adaptive disk optimization. In this work we initiate the study of this problem in the competitive setting. Our main result is showing nontrivial upper bounds on the competitive ratio. For restricted access patterns we give algorithms that have much better competitive ratios. To complement those bounds we show that there is no constantcompetitive algorithm for the problem with arbitrary access patterns, even against an adversary that does not rearrange its items. Department of Computer Science, Tel Aviv University, Tel Aviv. Research supported in part by a grant from the Israel Academy of Sciences. EM...
On the competitiveness of the movetofront rule
, 2000
"... We consider the list access problem and show that one questionable assumption in the original cost model presented by Sleator and Tarjan (1985) and subsequent literature allowed for several competitiveness results of the movetofront rule (MTF). We present an oline algorithm for the list access p ..."
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Cited by 4 (0 self)
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We consider the list access problem and show that one questionable assumption in the original cost model presented by Sleator and Tarjan (1985) and subsequent literature allowed for several competitiveness results of the movetofront rule (MTF). We present an oline algorithm for the list access problem and prove that, under a more realistic cost model, no online algorithm