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Speeding Up The Computations On An Elliptic Curve Using AdditionSubtraction Chains
 Theoretical Informatics and Applications
, 1990
"... We show how to compute x k using multiplications and divisions. We use this method in the context of elliptic curves for which a law exists with the property that division has the same cost as multiplication. Our best algorithm is 11.11% faster than the ordinary binary algorithm and speeds up acco ..."
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Cited by 109 (4 self)
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We show how to compute x k using multiplications and divisions. We use this method in the context of elliptic curves for which a law exists with the property that division has the same cost as multiplication. Our best algorithm is 11.11% faster than the ordinary binary algorithm and speeds up accordingly the factorization and primality testing algorithms using elliptic curves. 1. Introduction. Recent algorithms used in primality testing and integer factorization make use of elliptic curves defined over finite fields or Artinian rings (cf. Section 2). One can define over these sets an abelian law. As a consequence, one can transpose over the corresponding groups all the classical algorithms that were designed over Z/NZ. In particular, one has the analogue of the p \Gamma 1 factorization algorithm of Pollard [29, 5, 20, 22], the Fermatlike primality testing algorithms [1, 14, 21, 26] and the public key cryptosystems based on RSA [30, 17, 19]. The basic operation performed on an elli...
The Mungi singleaddressspace operating system
 Software— Practice and Experience
, 1998
"... Abstract Singleaddressspace operating systems (SASOS) are an attractive model for making the best use of the wide address space provided by the latest generations of microprocessors. SASOS remove the address space boundaries which make data sharing between processes difficult and expensive in trad ..."
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Cited by 64 (17 self)
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Abstract Singleaddressspace operating systems (SASOS) are an attractive model for making the best use of the wide address space provided by the latest generations of microprocessors. SASOS remove the address space boundaries which make data sharing between processes difficult and expensive in traditional operating systems. They offer the potential of significant performance advantages for applications where sharing is important, such as objectoriented databases or persistent programming systems. We have built the Mungi system to demonstrate that a SASOS can offer these performance advantages without resorting to special hardware. Mungi is a very "pure " SASOS, featuring an unintrusive protection model based on sparse capabilities, a fast protected procedure call mechanism, and uses shared memory as the exclusive interprocess communication mechanism, as well as for I/O. The simplicity of our model makes it easy to implement it efficiently on conventional architectures.
A compact space decomposition for effective metric indexing
 Pattern Recognition Letters
, 2005
"... Abstract The metric space model abstracts many proximity search problems, from nearestneighborclassifiers to textual and multimedia information retrieval. In this context, an index is a data structure that speeds up proximity queries. However, indexes lose their efficiency as the intrinsicdata dime ..."
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Cited by 41 (8 self)
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Abstract The metric space model abstracts many proximity search problems, from nearestneighborclassifiers to textual and multimedia information retrieval. In this context, an index is a data structure that speeds up proximity queries. However, indexes lose their efficiency as the intrinsicdata dimensionality increases. In this paper we present a simple index called list of clusters (LC), which is based on a compact partitioning of the data set. The LC is shown to require little space,to be suitable both for main and secondary memory implementations, and most importantly, to be very resistant to the intrinsic dimensionality of the data set. In this aspect our structure isunbeaten. We finish with a discussion of the role of unbalancing in metric space searching, and how it permits trading memory space for construction time. 1 Introduction The problem of proximity searching has received much attention in recent times, due to an increasing interest in manipulating and retrieving the more and more common multimedia data. Multimedia data have to be classified, forecasted, filtered, organized, and so on. Their manipulation poses new challenges to classifiers and function approximators. The wellknown knearest neighbor (knn) classifier is a favorite candidate for this task for being simple enough and well understood. One of the main obstacles, however, of using this classifier for massive data classification is its linear complexity to find a set of k neighbors for a given query.
TREE COMPRESSION AND OPTIMIZATION WITH APPLICATIONS
, 1990
"... Different methods for compressing trees are surveyed and developed. Tree compression can be seen as a tradeoff problem between time and space in which we can choose different strategies depending on whether we prefer better compression results or more efficient operations in the compressed structur ..."
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Cited by 25 (0 self)
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Different methods for compressing trees are surveyed and developed. Tree compression can be seen as a tradeoff problem between time and space in which we can choose different strategies depending on whether we prefer better compression results or more efficient operations in the compressed structure. Of special interest is the case where space can be saved while preserving the functionality of the operations; this is called data optimization. The general compression scheme employed here consists of separate linearization of the tree structure and the data stored in the tree. Also some applications of the tree compression methods are explored. These include the syntaxdirected compression of program files, the compression of pixel trees, trie compaction and dictionaries maintained as implicit data structures.
Approximate Text Searching
, 1998
"... This thesis focuses on the problem of text retrieval allowing errors, also called \approximate " string matching. The problem is to nd a pattern in a text, where the pattern and the text may have \errors". This problem has received a lot of attention in recent years because of its applicat ..."
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Cited by 22 (6 self)
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This thesis focuses on the problem of text retrieval allowing errors, also called \approximate " string matching. The problem is to nd a pattern in a text, where the pattern and the text may have \errors". This problem has received a lot of attention in recent years because of its applications in many areas, such as information retrieval, computational biology and signal processing, to name a few. The aim of this work is the development and analysis of novel algorithms to deal with the problem under various conditions, as well as a better understanding of the problem itself and its statistical behavior. Although our results are valid in many dierent areas, we focus our attention on typical text searching for information retrieval applications. This makes some ranges of values for the parameters of the problem more interesting than others. We have divided this presentation in two parts. The rst one deals with online approximate string matching, i.e. when there is no time or space to preprocess the text. These algorithms are the core of oline algorithms as well. Online searching is the area of the problem where better algorithms existed. We have obtained new bounds for the probability of an approximate match of a pattern in
MultiMethod Dispatching: A Geometric Approach with Applications to String Matching Problems
, 1999
"... Current object oriented programming languages (OOPLs) rely on monomethod dispatching. Recent research has identified multimethods as a new, powerful feature to be added to OOPLs, and several experimental OOPLs now have multimethods. Their ultimate success and impact in practice depends, among ..."
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Cited by 20 (3 self)
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Current object oriented programming languages (OOPLs) rely on monomethod dispatching. Recent research has identified multimethods as a new, powerful feature to be added to OOPLs, and several experimental OOPLs now have multimethods. Their ultimate success and impact in practice depends, among other things, on whether multimethod dispatching can be supported efficiently. We show that the multimethod dispatching problem can be transformed to a geometric problem on multidimensional integer grids, for which we then develop a data structure that uses nearlinear space and has O(log log n) query time. This gives a solution whose performance almost matches that of the best known algorithm for standard monomethod dispatching. Our geometric data structure has other applications as well, namely in two string matching problems: matching multiple rectangular patterns against a rectangular query text, and approximate dictionary matching with edit distance at most one. Our results f...
Triejoin: a triebased method for efficient string similarity joins
 THE VLDB JOURNAL
, 2012
"... A string similarity join finds similar pairs between two collections of strings. Many applications, e.g., data integration and cleaning, can significantly benefit from an efficient stringsimilarityjoin algorithm. In this paper, we study string similarity joins with editdistance constraints. Exis ..."
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Cited by 12 (5 self)
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A string similarity join finds similar pairs between two collections of strings. Many applications, e.g., data integration and cleaning, can significantly benefit from an efficient stringsimilarityjoin algorithm. In this paper, we study string similarity joins with editdistance constraints. Existing methods usually employ a filterandrefine framework and suffer from the following limitations: (1) They are inefficient for the data sets with short strings (the average string length is not larger than 30); (2) They involve large indexes; (3) They are expensive to support dynamic update of data sets. To address these problems, we propose a novel method called triejoin, which can generate results efficiently with small indexes. We use a trie structure to index the strings and utilize the trie structure to efficiently find similar string pairs based on subtrie pruning. We devise efficient triejoin algorithms and pruning techniques to achieve high performance. Our method can be easily extended to support dynamic update of data sets efficiently. We conducted extensive experiments on four real data sets. Experimental results show that our algorithms outperform stateoftheart methods by an order of magnitude on the data sets with short strings.
Optimal incremental sorting
 In Proc. 8th Workshop on Algorithm Engineering and Experiments (ALENEX
, 2006
"... Let A be a set of size m. Obtaining the first k ≤ m elements of A in ascending order can be done in optimal O(m+k log k) time. We present an algorithm (online on k) which incrementally gives the next smallest element of the set, so that the first k elements are obtained in optimal time for any k. We ..."
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Cited by 9 (5 self)
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Let A be a set of size m. Obtaining the first k ≤ m elements of A in ascending order can be done in optimal O(m+k log k) time. We present an algorithm (online on k) which incrementally gives the next smallest element of the set, so that the first k elements are obtained in optimal time for any k. We also give a practical algorithm with the same complexity on average, which improves in practice the existing online algorithm. As a direct application, we use our technique to implement Kruskal’s Minimum Spanning Tree algorithm, where our solution is competitive with the best current implementations. We finally show that our technique can be applied to several other problems, such as obtaining an interval of the sorted sequence and implementing heaps. 1
Searching the Web: Challenges and Partial Solutions
"... In this article we analyze the problem of searching the WWW, giving some insight and models to understand its complexity. Then we survey the two main current techniques used to search the WWW. Finally, we present recent results that can help to partially solve the challenges posed. 1. Introduction ..."
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Cited by 3 (0 self)
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In this article we analyze the problem of searching the WWW, giving some insight and models to understand its complexity. Then we survey the two main current techniques used to search the WWW. Finally, we present recent results that can help to partially solve the challenges posed. 1. Introduction The boom in the use of the World Wide Web (WWW) and its exponential growth are well known facts nowadays. Just the amount of textual data available is estimated in the order of one terabyte. In addition, other media, as images, audio and video, are also available. Thus, the WWW can be seen as a very large, unstructured but ubiquitous database. This triggers the need for efficient tools to manage, retrieve, and filter information from this database. This problem is also becoming important in large Intranets, where we want to extract or infer new information to support a decision process. This task is called data mining. We make the important distinction between data and information. The late...