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A Parallel Algorithm for Interpolation in Pancake Graph
"... Abstract: In this paper a parallel algorithm for Lagrange interpolation is applied on a npancake graph. The npancake graph is a Cayley graph with N=n! vertices and with attractive properties regarding degree, diameter, symmetry, embeddings and self similarity. Using these properties the algorithm c ..."
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Abstract: In this paper a parallel algorithm for Lagrange interpolation is applied on a npancake graph. The npancake graph is a Cayley graph with N=n! vertices and with attractive properties regarding degree, diameter, symmetry, embeddings and self similarity. Using these properties the algorithm
Fault Tolerant Routing in the Star and Pancake Interconnection Networks
 Information Processing Letters
"... this paper is to show that a recently proposed interconnection network enjoys similar properties. We will prove that if S n is the nstar graph then for any minimal length routing ae the diameter D(R(S n ; ae)=F ) is at most 3, as long as jF j ! n. Moreover, we will prove that if P n is the npancak ..."
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Cited by 9 (0 self)
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this paper is to show that a recently proposed interconnection network enjoys similar properties. We will prove that if S n is the nstar graph then for any minimal length routing ae the diameter D(R(S n ; ae)=F ) is at most 3, as long as jF j ! n. Moreover, we will prove that if P n is the npancake
The Landscape of Parallel Computing Research: A View from Berkeley
 TECHNICAL REPORT, UC BERKELEY
, 2006
"... ..."
The nDimensional Burnt Pancake Graph is n∗connected
 THE 25TH WORKSHOP ON COMBINATORIAL MATHEMATICS AND COMPUTATION THEORY
"... A kcontainer C(u, v) of a graph G is a set of kdisjoint paths joining u to v. A kcontainer C(u, v) of G is k ∗container if C(u, v) spans G. A graph G is k ∗connected if there exists a k ∗container between any two distinct vertices. Let κ(G) be the connectivity of G. In this paper, we prove tha ..."
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that the ndimensional burnt pancake graph Bn is n∗connected for any positive integer n.
Survey of Polygonal Surface Simplification Algorithms
, 1997
"... This paper surveys methods for simplifying and approximating polygonal surfaces. A polygonal surface is a piecewiselinear surface in 3D defined by a set of polygons ..."
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Cited by 228 (3 self)
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This paper surveys methods for simplifying and approximating polygonal surfaces. A polygonal surface is a piecewiselinear surface in 3D defined by a set of polygons
Cayley Graphs and Interconnection Networks
, 1997
"... In this report, we will focus on routing problems including connectivity, diameter and loads of routings. We place the emphasis on load problems, since new classes of vertextransitive graphs (see quasiCayley graphs in Section 5.3) or edgetransitive graphs (see regular orbital graphs in Section 5. ..."
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Cited by 72 (3 self)
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In this report, we will focus on routing problems including connectivity, diameter and loads of routings. We place the emphasis on load problems, since new classes of vertextransitive graphs (see quasiCayley graphs in Section 5.3) or edgetransitive graphs (see regular orbital graphs in Section 5
An Elementary Introduction to Modern Convex Geometry
 in Flavors of Geometry
, 1997
"... Introduction to Modern Convex Geometry KEITH BALL Contents Preface 1 Lecture 1. Basic Notions 2 Lecture 2. Spherical Sections of the Cube 8 Lecture 3. Fritz John's Theorem 13 Lecture 4. Volume Ratios and Spherical Sections of the Octahedron 19 Lecture 5. The BrunnMinkowski Inequality and It ..."
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Cited by 171 (3 self)
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Introduction to Modern Convex Geometry KEITH BALL Contents Preface 1 Lecture 1. Basic Notions 2 Lecture 2. Spherical Sections of the Cube 8 Lecture 3. Fritz John's Theorem 13 Lecture 4. Volume Ratios and Spherical Sections of the Octahedron 19 Lecture 5. The BrunnMinkowski Inequality and Its Extensions 25 Lecture 6. Convolutions and Volume Ratios: The Reverse Isoperimetric Problem 32 Lecture 7. The Central Limit Theorem and Large Deviation Inequalities 37 Lecture 8. Concentration of Measure in Geometry 41 Lecture 9. Dvoretzky's Theorem 47 Acknowledgements 53 References 53 Index 55 Preface These notes are based, somewhat loosely, on three series of lectures given by myself, J. Lindenstrauss and G. Schechtman, during the Introductory Workshop in Convex Geometry held at the Mathematical Sciences Research Institute in Berkeley, early in 1996. A fourth series was given by B. Bollobas, on rapid mixing and random volume algorithms; they are found els
Embedding of Meshes on Rotator Graphs
, 1993
"... A set of directed permutation graphs called rotator graphs were proposed as an alternative to the star and pancake graphs for multiprocessor interconnection networks. The rotator graphs have a smaller diameter than star and pancake graphs for the same number of nodes, while sharing the properties of ..."
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of star, pancake, and binary hypercubes like maximal fault tolerance, partitionability, etc. In this paper we develop a class of algorithms for recognizing undirected mesh structures in nrotator graphs. The average dilation of the embeddings are very low as compared to the dilation of the embedding
On VLSI Layouts Of The Star Graph And Related Networks
, 1994
"... . We prove that the minimal VLSI layout of the arrangement graph A(n; k) occupies \Theta(n!=(n \Gamma k \Gamma 1)!) 2 area. As a special case we obtain an optimal layout for the star graph S n with the area \Theta(n!) 2 : This answers an open problem posed by Akers, Harel and Krishnamurthy [1]. ..."
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Cited by 18 (3 self)
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. We prove that the minimal VLSI layout of the arrangement graph A(n; k) occupies \Theta(n!=(n \Gamma k \Gamma 1)!) 2 area. As a special case we obtain an optimal layout for the star graph S n with the area \Theta(n!) 2 : This answers an open problem posed by Akers, Harel and Krishnamurthy [1
Hamiltonian Paths and Cycles in Faulty Burnt Pancake Graphs
"... Abstract Recently, research on parallel processing systems is very active, and many complex topologies have been proposed. A burnt pancake graph is one such topology. In this paper, we prove that a faulty burnt pancake graph with degree n has a faultfree Hamiltonian cycle if the number of faulty el ..."
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Abstract Recently, research on parallel processing systems is very active, and many complex topologies have been proposed. A burnt pancake graph is one such topology. In this paper, we prove that a faulty burnt pancake graph with degree n has a faultfree Hamiltonian cycle if the number of faulty
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