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20
Dynamical Sources in Information Theory: A General Analysis of Trie Structures
 ALGORITHMICA
, 1999
"... Digital trees, also known as tries, are a general purpose flexible data structure that implements dictionaries built on sets of words. An analysis is given of three major representations of tries in the form of arraytries, list tries, and bsttries ("ternary search tries"). The size and the sear ..."
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Cited by 50 (7 self)
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Digital trees, also known as tries, are a general purpose flexible data structure that implements dictionaries built on sets of words. An analysis is given of three major representations of tries in the form of arraytries, list tries, and bsttries ("ternary search tries"). The size and the search costs of the corresponding representations are analysed precisely in the average case, while a complete distributional analysis of height of tries is given. The unifying data model used is that of dynamical sources and it encompasses classical models like those of memoryless sources with independent symbols, of finite Markovchains, and of nonuniform densities. The probabilistic behaviour of the main parameters, namely size, path length, or height, appears to be determined by two intrinsic characteristics of the source: the entropy and the probability of letter coincidence. These characteristics are themselves related in a natural way to spectral properties of specific transfer operators of the Ruelle type.
Selfimproving algorithms
 in SODA ’06: Proceedings of the seventeenth annual ACMSIAM symposium on Discrete algorithm
"... We investigate ways in which an algorithm can improve its expected performance by finetuning itself automatically with respect to an arbitrary, unknown input distribution. We give such selfimproving algorithms for sorting and computing Delaunay triangulations. The highlights of this work: (i) an al ..."
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Cited by 26 (4 self)
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We investigate ways in which an algorithm can improve its expected performance by finetuning itself automatically with respect to an arbitrary, unknown input distribution. We give such selfimproving algorithms for sorting and computing Delaunay triangulations. The highlights of this work: (i) an algorithm to sort a list of numbers with optimal expected limiting complexity; and (ii) an algorithm to compute the Delaunay triangulation of a set of points with optimal expected limiting complexity. In both cases, the algorithm begins with a training phase during which it adjusts itself to the input distribution, followed by a stationary regime in which the algorithm settles to its optimized incarnation. 1
The Analysis of Hybrid Trie Structures
, 1998
"... This paper provides a detailed analysis of various implementations of digital tries, including the “ternary search tries” of Bentley and Sedgewick. The methods employed combine symbolic uses of generating functions, Poisson models, and MeIlin transforms. Theoretical results are matched against real ..."
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Cited by 24 (2 self)
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This paper provides a detailed analysis of various implementations of digital tries, including the “ternary search tries” of Bentley and Sedgewick. The methods employed combine symbolic uses of generating functions, Poisson models, and MeIlin transforms. Theoretical results are matched against reallife data and justify the claim that ternary search tries are a highly efficient dynamic dictionary structure for strings and textual data.
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...
An Evaluation of Selfadjusting Binary Search Tree Techniques
 Software Practice and Experience
, 1993
"... Much has been said in praise of... this paper, we compare the performance of three different techniques for selfadjusting trees with that of AVL and random binary search trees. Comparisons are made for various tree sizes, levels of keyaccessfrequency skewness and ratios of insertions and deletion ..."
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Cited by 17 (1 self)
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Much has been said in praise of... this paper, we compare the performance of three different techniques for selfadjusting trees with that of AVL and random binary search trees. Comparisons are made for various tree sizes, levels of keyaccessfrequency skewness and ratios of insertions and deletions to searches. The results show that, because of the high cost of maintaining selfadjusting trees, in almost all cases the AVL tree outperforms all the selfadjusting trees and in many cases even a random binary search tree has better performance, in terms of CPU time, than any of the selfadjusting trees. Selfadjusting trees seem to perform best in a highly dynamic environment, contrary to intuition.
Power Laws in Software
"... A single statistical framework, comprising power law distributions and scalefree networks, seems to fit a wide variety of phenomena. There is evidence that power laws appear in software at the class and function level. We show that distributions with long, fat tails in software are much more pervas ..."
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Cited by 11 (0 self)
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A single statistical framework, comprising power law distributions and scalefree networks, seems to fit a wide variety of phenomena. There is evidence that power laws appear in software at the class and function level. We show that distributions with long, fat tails in software are much more pervasive than previously established, appearing at various levels of abstraction, in diverse systems and languages. The implications of this phenomenon cover various aspects of software engineering research and practice.
On the Markov chain for the movetoroot rule for binary search trees
, 1998
"... The movetoroot (MTR) heuristic is a selforganizing rule which attempts to keep a binary search tree in nearoptimal form. It is a tree analogue of the movetofront (MTF) scheme for selforganizing lists. Both heuristics can be modeled as Markov chains. We show that the MTR chain can be deriv ..."
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Cited by 9 (3 self)
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The movetoroot (MTR) heuristic is a selforganizing rule which attempts to keep a binary search tree in nearoptimal form. It is a tree analogue of the movetofront (MTF) scheme for selforganizing lists. Both heuristics can be modeled as Markov chains. We show that the MTR chain can be derived by lumping the MTF chain and give exact formulas for the transition probabilities and stationary distribution for MTR. We also derive the eigenvalues and their multiplicities for MTR. 1 Research for both authors supported by NSF grant DMS9311367. 2 AMS 1991 subject classifications. Primary 60J10; secondary 68P10, 68P05. 3 Keywords and phrases. Markov chains, selforganizing search, binary search trees, movetoroot rule, lumping, eigenvalues, simple exchange, movetofront rule. 1 1 Introduction and Summary There has been much interest in recent years in selforganizing search methods. Hester and Hirschberg (1985) survey the field. Hendricks (1989) is a good introduction with...
Adaptive Heuristics for Binary Search Trees and Constant Linkage Cost
 In Proc. of the 2nd ACMSIAM Symposium on Discrete Algorithms
, 1995
"... We present lower and upper bounds on adaptive heuristics for maintaining binary search trees using a constant number of link or pointer changes for each operation (constant linkage cost (CLC)). We show that no adaptive heuristic with an amortized linkage cost of o(log n) can be competitive. In part ..."
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Cited by 8 (0 self)
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We present lower and upper bounds on adaptive heuristics for maintaining binary search trees using a constant number of link or pointer changes for each operation (constant linkage cost (CLC)). We show that no adaptive heuristic with an amortized linkage cost of o(log n) can be competitive. In particular, we show that any heuristic that performs f(n) = o(log n) promotions (rotations) amortized over each access has a competitive ratio of at least \Omega\Gammaast n=f(n)) against an oblivious adversary, and any heuristic that performs f(n) = o(log n) pointer changes amortized over each access has a competitive ratio of at least\Omega\Gamma log n f(n) log(log n=f(n)) ) against an adaptive online adversary. In our investigation of upper bounds we present four adaptive heuristics: ffl A randomized, worstcaseCLC heuristic (R2P) whose expected search time is within a constant factor of the search time using an optimal tree; that is, it is statically competitive ffl A randomized, expecte...
Adaptive Structuring Of Binary Search Trees Using Conditional Rotations
 IEEE TRANSACTIONS ON KNOWLEDGE & DATA ENGINEERING
, 1987
"... Consider a set A = {A 1 , A 2 ,...,A N } of records, where each record is identified by a unique key. The records are accessed based on a set of access probabilities S = [s 1 ,s 2 ,...,s N ] and are to be arranged lexicographically using a Binary Search Tree (BST). If S is known a priori, it ..."
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Cited by 6 (2 self)
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Consider a set A = {A 1 , A 2 ,...,A N } of records, where each record is identified by a unique key. The records are accessed based on a set of access probabilities S = [s 1 ,s 2 ,...,s N ] and are to be arranged lexicographically using a Binary Search Tree (BST). If S is known a priori, it is well known [10] that an optimal BST may be constructed using A and S. We consider the case when S is not known a priori . A new restructuring heuristic is introduced that requires three extra integer memory locations per record. In this scheme the restructuring is performed only if it decreases the Weighted Path Length (WPL) of the overall resultant tree. An optimized version of the latter method which requires only one extra integer field per record has also been presented. Initial simulation results which compare our algorithm with various other static and dynamic schemes seem to indicate that this scheme asymptotically produces trees which are an order of magnitude closer to the optim...
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.