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47
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 33 (12 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.
Second step algorithms in the BurrowsWheeler compression algorithm
 Software Practice and Experience
, 2001
"... In this paper we fix our attention on the second step algorithms of the BurrowsWheeler compression algorithm, which in the original version is the Move To Front transform. We discuss many of its replacements presented so far, and compare compression results obtained using them. Then we propose ..."
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Cited by 29 (0 self)
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In this paper we fix our attention on the second step algorithms of the BurrowsWheeler compression algorithm, which in the original version is the Move To Front transform. We discuss many of its replacements presented so far, and compare compression results obtained using them. Then we propose a new algorithm that yields a better compression ratio than the previous ones.
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 22 (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 22 (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...
Splay trees, DavenportSchinzel sequences, and the deque conjecture
"... We introduce a new technique to bound the asymptotic performance of splay trees. The basic idea is to transcribe, in an indirect fashion, the rotations performed by the splay tree as a DavenportSchinzel sequence, none of whose subsequences are isomorphic to a fixed forbidden subsequence. We direct ..."
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Cited by 18 (6 self)
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We introduce a new technique to bound the asymptotic performance of splay trees. The basic idea is to transcribe, in an indirect fashion, the rotations performed by the splay tree as a DavenportSchinzel sequence, none of whose subsequences are isomorphic to a fixed forbidden subsequence. We direct this technique towards Tarjan’s deque conjecture and prove that n deque operations take only O(nα ∗ (n)) time, where α ∗ (n) is the minimum number of applications of the inverseAckermann function mapping n to a constant. We are optimistic that this approach could be directed towards other open conjectures on splay trees such as the traversal and split conjectures.
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 17 (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...
Improvements to BurrowsWheeler Compression Algorithm
, 2000
"... In 1994 Burrows and Wheeler presented a new algorithm for lossless data compression. The compression ratio that can be achieved using their algorithm is comparable with the best known other algorithms, whilst its complexity is relatively small. In this paper we explain the internals of this algorith ..."
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Cited by 14 (3 self)
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In 1994 Burrows and Wheeler presented a new algorithm for lossless data compression. The compression ratio that can be achieved using their algorithm is comparable with the best known other algorithms, whilst its complexity is relatively small. In this paper we explain the internals of this algorithm and discuss its various modifications that have been presented so far. Then we propose new improvements for its effectiveness. They allow us for obtaining the compression ratio equal to 2.271 bpc for the Calgary Corpus files, which is the best result in the class of BurrowsWheeler Transform based algorithms.
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 14 (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.
Two New Families of List Update Algorithms
 In ISSAC'98, LCNS 1533
, 1998
"... . We consider the online list accessing problem and present a new family of competitiveoptimal deterministic list update algorithms which is the largest class of such algorithms known todate. This family, called SortbyRank (sbr), is parametrized with a real 0 ff 1, where sbr(0) is the Move ..."
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Cited by 8 (0 self)
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. We consider the online list accessing problem and present a new family of competitiveoptimal deterministic list update algorithms which is the largest class of such algorithms known todate. This family, called SortbyRank (sbr), is parametrized with a real 0 ff 1, where sbr(0) is the MovetoFront algorithm and sbr(1) is equivalent to the Timestamp algorithm. The behaviour of sbr(ff) mediates between the eager strategy of MovetoFront and the more conservative behaviour of Timestamp. We also present a family of algorithms SortbyDelay (sbd) which is parametrized by the positive integers, where sbd(1) is MovetoFront and sbd(2) is equivalent to Timestamp. In general, sbd(k) is kcompetitive for k 2. This is the first class of algorithms that is asymptotically optimal for independent, identically distributed requests while each algorithm is constantcompetitive. Empirical studies with with both generated and realworld data are also included. 1 Introduction Co...
Dynamic Optimality for Skip Lists and BTrees
, 2008
"... Sleator and Tarjan [39] conjectured that splay trees are dynamically optimal binary search trees (BST). In this context, we study the skip list data structure introduced by Pugh [35]. We prove that for a class of skip lists that satisfy a weak balancing property, the workingset bound is a lower bou ..."
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Cited by 7 (2 self)
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Sleator and Tarjan [39] conjectured that splay trees are dynamically optimal binary search trees (BST). In this context, we study the skip list data structure introduced by Pugh [35]. We prove that for a class of skip lists that satisfy a weak balancing property, the workingset bound is a lower bound on the time to access any sequence. Furthermore, we develop a deterministic selfadjusting skip list whose running time matches the workingset bound, thereby achieving dynamic optimality in this class. Finally, we highlight the implications our bounds for skip lists have on multiway branching search trees such as Btrees, (ab)trees, and other variants as well as their binary tree representations. In particular, we show a selfadjusting Btree that is dynamically optimal both in internal and external memory.