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New directions in cryptography.
 IEEE Trans. Inf. Theory,
, 1976
"... Abstract Two kinds of contemporary developments in crypcommunications over an insecure channel order to use cryptogtography are examined. Widening applications of teleprocessraphy to insure privacy, however, it currently necessary for the ing have given rise to a need for new types of cryptograph ..."
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Cited by 3542 (7 self)
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Abstract Two kinds of contemporary developments in crypcommunications over an insecure channel order to use cryptogtography are examined. Widening applications of teleprocessraphy to insure privacy, however, it currently necessary for the ing have given rise to a need for new types of cryptographic communicating parties to share a key which is known to no systems, which minimize the need for secure key distribution one else. This is done by sending the key in advance over some channels and supply the equivalent of a written signature. This secure channel such a private courier or registered mail. A paper suggests ways to solve these currently open problems. private conversation between two people with no prior acquainIt also discusses how the theories of communication and computance is a common occurrence in business, however, and it is tation are beginning to provide the tools to solve cryptographic unrealistic to expect initial business contacts to be postponed problems of long standing. long enough for keys to be transmitted by some physical means. The cost and delay imposed by this key distribution problem is a major barrier to the transfer of business communications
Information Theory and Statistics
, 1968
"... Entropy and relative entropy are proposed as features extracted from symbol sequences. Firstly, a proper Iterated Function System is driven by the sequence, producing a fractaMike representation (CSR) with a low computational cost. Then, two entropic measures are applied to the CSR histogram of th ..."
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Cited by 1805 (2 self)
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Entropy and relative entropy are proposed as features extracted from symbol sequences. Firstly, a proper Iterated Function System is driven by the sequence, producing a fractaMike representation (CSR) with a low computational cost. Then, two entropic measures are applied to the CSR histogram of the CSR and theoretically justified. Examples are included.
Factoring polynomials with rational coefficients
 MATH. ANN
, 1982
"... In this paper we present a polynomialtime algorithm to solve the following problem: given a nonzero polynomial fe Q[X] in one variable with rational coefficients, find the decomposition of f into irreducible factors in Q[X]. It is well known that this is equivalent to factoring primitive polynomia ..."
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Cited by 961 (11 self)
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In this paper we present a polynomialtime algorithm to solve the following problem: given a nonzero polynomial fe Q[X] in one variable with rational coefficients, find the decomposition of f into irreducible factors in Q[X]. It is well known that this is equivalent to factoring primitive polynomials feZ[X] into irreducible factors in Z[X]. Here we call f ~ Z[X] primitive if the greatest common divisor of its coefficients (the content of f) is 1. Our algorithm performs well in practice, cf. [8]. Its running time, measured in bit operations, is O(nl2+n9(log[fD3). Here f~Tl[X] is the polynomial to be factored, n = deg(f) is the degree of f, and for a polynomial ~ a ~ i with real coefficients a i. i An outline of the algorithm is as follows. First we find, for a suitable small prime number p, a padic irreducible factor h of f, to a certain precision. This is done with Berlekamp's algorithm for factoring polynomials over small finite fields, combined with Hensel's lemma. Next we look for the irreducible factor h o of f in
Fibonacci Heaps and Their Uses in Improved Network optimization algorithms
, 1987
"... In this paper we develop a new data structure for implementing heaps (priority queues). Our structure, Fibonacci heaps (abbreviated Fheaps), extends the binomial queues proposed by Vuillemin and studied further by Brown. Fheaps support arbitrary deletion from an nitem heap in qlogn) amortized tim ..."
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Cited by 739 (18 self)
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In this paper we develop a new data structure for implementing heaps (priority queues). Our structure, Fibonacci heaps (abbreviated Fheaps), extends the binomial queues proposed by Vuillemin and studied further by Brown. Fheaps support arbitrary deletion from an nitem heap in qlogn) amortized time and all other standard heap operations in o ( 1) amortized time. Using Fheaps we are able to obtain improved running times for several network optimization algorithms. In particular, we obtain the following worstcase bounds, where n is the number of vertices and m the number of edges in the problem graph: ( 1) O(n log n + m) for the singlesource shortest path problem with nonnegative edge lengths, improved from O(m logfmh+2)n); (2) O(n*log n + nm) for the allpairs shortest path problem, improved from O(nm lo&,,,+2,n); (3) O(n*logn + nm) for the assignment problem (weighted bipartite matching), improved from O(nm log0dn+2)n); (4) O(mj3(m, n)) for the minimum spanning tree problem, improved from O(mloglo&,,.+2,n), where j3(m, n) = min {i 1 log % 5 m/n). Note that B(m, n) 5 log*n if m 2 n. Of these results, the improved bound for minimum spanning trees is the most striking, although all the
Tensor Decompositions and Applications
 SIAM REVIEW
, 2009
"... This survey provides an overview of higherorder tensor decompositions, their applications, and available software. A tensor is a multidimensional or N way array. Decompositions of higherorder tensors (i.e., N way arrays with N â¥ 3) have applications in psychometrics, chemometrics, signal proce ..."
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Cited by 723 (18 self)
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This survey provides an overview of higherorder tensor decompositions, their applications, and available software. A tensor is a multidimensional or N way array. Decompositions of higherorder tensors (i.e., N way arrays with N â¥ 3) have applications in psychometrics, chemometrics, signal processing, numerical linear algebra, computer vision, numerical analysis, data mining, neuroscience, graph analysis, etc. Two particular tensor decompositions can be considered to be higherorder extensions of the matrix singular value decompo
sition: CANDECOMP/PARAFAC (CP) decomposes a tensor as a sum of rankone tensors, and the Tucker decomposition is a higherorder form of principal components analysis. There are many other tensor decompositions, including INDSCAL, PARAFAC2, CANDELINC, DEDICOM, and PARATUCK2 as well as nonnegative variants of all of the above. The Nway Toolbox and Tensor Toolbox, both for MATLAB, and the Multilinear Engine are examples of software packages for working with tensors.
Automating the Design of Graphical Presentations of Relational Information
 ACM Transactions on Graphics
, 1986
"... The goal of the research described in this paper is to develop an applicationindependent presentation tool that automatically designs effective graphical presentations (such as bar charts, scatter plots, and connected graphs) of relational information. Two problems are raised by this goal: The codi ..."
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Cited by 559 (9 self)
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The goal of the research described in this paper is to develop an applicationindependent presentation tool that automatically designs effective graphical presentations (such as bar charts, scatter plots, and connected graphs) of relational information. Two problems are raised by this goal: The codification of graphic design criteria in a form that can be used by the presentation tool, and the generation of a wide variety of designs so that the presentation tool can accommodate a wide variety of information. The approach described in this paper is based on the view that graphical presentations are sentences of graphical languages. The graphic design issues are codified as expressiveness and effectiveness criteria for graphical languages. Expressiveness criteria determine whether a graphical language can express the desired information. Effectiveness criteria determine whether a graphical language exploits the capabilities of the output medium and the human visual system. A wide variety of designs can be systematically generated by using a composition algebra that composes a small set of primitive graphical languages. Artificial intelligence techniques are used to implement a prototype presentation tool called APT (A Presentation Tool), which is based on the composition algebra and the graphic design criteria.
Expected Time Bounds for Selection
, 1975
"... A new selection algorithm is presented which is shown to be very efficient on the average, both theoretically and practically. The number of comparisons used to select the ith smallest of n numbers is n q min(i,ni) q o(n). A lower bound within 9 percent of the above formula is also derived. ..."
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Cited by 459 (4 self)
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A new selection algorithm is presented which is shown to be very efficient on the average, both theoretically and practically. The number of comparisons used to select the ith smallest of n numbers is n q min(i,ni) q o(n). A lower bound within 9 percent of the above formula is also derived.
Selfadjusting binary search trees
, 1985
"... The splay tree, a selfadjusting form of binary search tree, is developed and analyzed. The binary search tree is a data structure for representing tables and lists so that accessing, inserting, and deleting items is easy. On an nnode splay tree, all the standard search tree operations have an am ..."
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Cited by 432 (18 self)
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The splay tree, a selfadjusting form of binary search tree, is developed and analyzed. The binary search tree is a data structure for representing tables and lists so that accessing, inserting, and deleting items is easy. On an nnode splay tree, all the standard search tree operations have an amortized time bound of O(log n) per operation, where by “amortized time ” is meant the time per operation averaged over a worstcase sequence of operations. Thus splay trees are as efficient as balanced trees when total running time is the measure of interest. In addition, for sufficiently long access sequences, splay trees are as efficient, to within a constant factor, as static optimum search trees. The efftciency of splay trees comes not from an explicit structural constraint, as with balanced trees, but from applying a simple restructuring heuristic, called splaying, whenever the tree is accessed. Extensions of splaying give simplified forms of two other data structures: lexicographic or multidimensional search trees and link/ cut trees.