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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 96 (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 54 (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 27 (6 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.
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 15 (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...
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 7 (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 2 (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...
Searching the World Wide Web: Challenges and Partial
 Progress in Artificial Intelligence  IBERAMIA 98, 6th IberoAmerican Conference on AI, Lecture Notes in Computer Science
, 1998
"... 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 ..."
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Cited by 1 (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
FOCAS Automatic Catalog Matching Algorithms
"... This paper describes efficient algorithms that automatically take two or more catalogs of objects with instrumental coordinates and magnitudes and matches them. The challenges are that the instrumental coordinates may be only partially overlapping, at a different scale, rotated, or even inverted (fl ..."
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Cited by 1 (0 self)
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This paper describes efficient algorithms that automatically take two or more catalogs of objects with instrumental coordinates and magnitudes and matches them. The challenges are that the instrumental coordinates may be only partially overlapping, at a different scale, rotated, or even inverted (flipped). The object magnitudes may be derived from different passbands so that the relative magnitudes of the objects differ. Also, the catalog may not contain all the same objects due to differences in separating close objects or to partial overlap between images. Finally, the catalog positions and magnitudes are subject to noise in the images from which they were derived. The algorithms are applicable to any automated cataloging system. However, the implementation described here is part of the Faint Object Classification and Analysis System (FOCAS). FOCAS automatically produces catalogs of objects from digital images. The algorithms described here first take a subsample of the brightest obj...
Approximate Text Searching
, 1998
"... This thesis focuses on the problem of text retrieval allowing errors, also called "approximate" string matching. The problem is to find 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 m ..."
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This thesis focuses on the problem of text retrieval allowing errors, also called "approximate" string matching. The problem is to find 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 different 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 first one deals with online approximate string matching, i.e. when there is no time or space ...