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The Overlay of Lower Envelopes and its Applications
, 1995
"... ... "), for any " ? 0. This result has several applications: (i) a nearquadratic upper bound on the complexity of the region in 3 space enclosed between the lower envelope of one such collection of functions and the upper envelope of another collection; (ii) an efficient and simple divid ..."
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Cited by 15 (4 self)
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... "), for any " ? 0. This result has several applications: (i) a nearquadratic upper bound on the complexity of the region in 3 space enclosed between the lower envelope of one such collection of functions and the upper envelope of another collection; (ii) an efficient and simple
The Overlay of Lower Envelopes and its Applications
 Discrete Comput. Geom
, 1996
"... Let F and G be two collections of a total of n bivariate algebraic functions of constant maximum degree. The minimization diagrams of F , G are the planar maps obtained by the xyprojections of the lower envelopes of F , G, respectively. We show that the combinatorial complexity of the overlay of t ..."
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Let F and G be two collections of a total of n bivariate algebraic functions of constant maximum degree. The minimization diagrams of F , G are the planar maps obtained by the xyprojections of the lower envelopes of F , G, respectively. We show that the combinatorial complexity of the overlay
The Overlay ofLower Envelopes and its Applications
, 1994
"... Let F and G be two collections of a total of n bivariate algebraic functions of constant maximum degree. The minimization diagrams of F, G are the planar maps obtained by the xyprojections of the lower envelopes of F, G, respectively. We show that the combinatorial complexity of the overlay of the ..."
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Cited by 1 (0 self)
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Let F and G be two collections of a total of n bivariate algebraic functions of constant maximum degree. The minimization diagrams of F, G are the planar maps obtained by the xyprojections of the lower envelopes of F, G, respectively. We show that the combinatorial complexity of the overlay
Geometry © 1996 SpringerVerlag New York Inc. The Overlay of Lower Envelopes and Its Applications ∗
"... Abstract. Let F and G be two collections of a total of n (possibly partially defined) bivariate, algebraic functions of constant maximum degree. The minimization diagrams of F, G are the planar maps obtained by the xyprojections of the lower envelopes of F, G, respectively. We show that the combina ..."
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that the combinatorial complexity of the overlay of the minimization diagrams of F and of G is O(n 2+ε), for any ε>0. This result has several applications: (i) a nearquadratic upper bound on the complexity of the region in 3space enclosed between the lower envelope of one such collection of functions and the upper
Pushing the EL envelope
 In Proc. of IJCAI 2005
, 2005
"... Recently, it has been shown that the small description logic (DL) EL, which allows for conjunction and existential restrictions, has better algorithmic properties than its counterpart FL0, which allows for conjunction and value restrictions. Whereas the subsumption problem in FL0 becomes already int ..."
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Cited by 465 (60 self)
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Recently, it has been shown that the small description logic (DL) EL, which allows for conjunction and existential restrictions, has better algorithmic properties than its counterpart FL0, which allows for conjunction and value restrictions. Whereas the subsumption problem in FL0 becomes already
Multimarket Oligopoly: Strategic Substitutes and complements
 JOURNAL OF POLITICAL ECONOMY
"... A firm’s actions in one market can change competitors’ strategies in a second market by affecting its own marginal costs in that other market. Whether the action provides costs or benefits in the second market depends on (a) whether it increases or decreases marginal costs in the second market and ..."
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Cited by 601 (10 self)
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A firm’s actions in one market can change competitors’ strategies in a second market by affecting its own marginal costs in that other market. Whether the action provides costs or benefits in the second market depends on (a) whether it increases or decreases marginal costs in the second market
Topologicallyaware overlay construction and server selection
, 2002
"... A number of largescale distributed Internet applications could potentially benefit from some level of knowledge about the relative proximity between its participating host nodes. For example, the performance of large overlay networks could be improved if the applicationlevel connectivity between ..."
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Cited by 343 (5 self)
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A number of largescale distributed Internet applications could potentially benefit from some level of knowledge about the relative proximity between its participating host nodes. For example, the performance of large overlay networks could be improved if the applicationlevel connectivity
A highperformance, portable implementation of the MPI message passing interface standard
 Parallel Computing
, 1996
"... MPI (Message Passing Interface) is a specification for a standard library for message passing that was defined by the MPI Forum, a broadly based group of parallel computer vendors, library writers, and applications specialists. Multiple implementations of MPI have been developed. In this paper, we d ..."
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Cited by 888 (67 self)
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MPI (Message Passing Interface) is a specification for a standard library for message passing that was defined by the MPI Forum, a broadly based group of parallel computer vendors, library writers, and applications specialists. Multiple implementations of MPI have been developed. In this paper, we
Solving multiclass learning problems via errorcorrecting output codes
 JOURNAL OF ARTIFICIAL INTELLIGENCE RESEARCH
, 1995
"... Multiclass learning problems involve nding a de nition for an unknown function f(x) whose range is a discrete set containing k>2values (i.e., k \classes"). The de nition is acquired by studying collections of training examples of the form hx i;f(x i)i. Existing approaches to multiclass l ..."
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Cited by 730 (8 self)
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learning problems include direct application of multiclass algorithms such as the decisiontree algorithms C4.5 and CART, application of binary concept learning algorithms to learn individual binary functions for each of the k classes, and application of binary concept learning algorithms with distributed
Convex Analysis
, 1970
"... In this book we aim to present, in a unified framework, a broad spectrum of mathematical theory that has grown in connection with the study of problems of optimization, equilibrium, control, and stability of linear and nonlinear systems. The title Variational Analysis reflects this breadth. For a lo ..."
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Cited by 5350 (67 self)
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progressed also to the study of socalled stationary points, critical points, and other indications of singularity that a point might have relative to its neighbors, especially in association with existence theorems for differential equations.
Results 1  10
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