Teng, ShangHua
Overview
Works:  43 works in 80 publications in 1 language and 493 library holdings 

Genres:  Conference papers and proceedings 
Roles:  Author, Editor 
Publication Timeline
.
Most widely held works by
ShangHua Teng
Algorithms and computation : 11th international conference, ISAAC 2000, Taipei, Taiwan, December 1820, 2000 ; proceedings by
Gerhard Goos(
Book
)
15 editions published between 1999 and 2001 in English and held by 281 WorldCat member libraries worldwide
This book constitutes the refereed proceedings of the 11th International Conference on Algorithms and Computation, ISAAC 2000, held in Taipei, Taiwan in December 2000. The 46 revised papers presented together with an invited paper were carefully reviewed and selected from 87 submissions. The papers are organized in topical sections on algorithms and data structures; combinatorial optimization; approximation and randomized algorithms; graph drawing and graph algorithms; automata, cryptography, and complexity theory; parallel and distributed algorithms; computational geometry; and computational biology
15 editions published between 1999 and 2001 in English and held by 281 WorldCat member libraries worldwide
This book constitutes the refereed proceedings of the 11th International Conference on Algorithms and Computation, ISAAC 2000, held in Taipei, Taiwan in December 2000. The 46 revised papers presented together with an invited paper were carefully reviewed and selected from 87 submissions. The papers are organized in topical sections on algorithms and data structures; combinatorial optimization; approximation and randomized algorithms; graph drawing and graph algorithms; automata, cryptography, and complexity theory; parallel and distributed algorithms; computational geometry; and computational biology
Solving irregularly structured problems in parallel : 5th international symposium, IRREGULAR '98, Berkeley, California, USA,
August 1998 : proceedings by
Afonso Ferreira(
)
4 editions published in 1998 in English and held by 77 WorldCat member libraries worldwide
This book constitutes the refereed proceedings of the 5th International Symposium on Solving Irregularly Structured Problems in Parallel, IRREGULAR'98, held in Berkeley, California, in August 1998. The 26 revised full papers presented were carefully reviewed and selected for inclusion from several dozen submissions. Also included are abstracts of four invited talks and 6 invited presentations given during minisymposia held in parallel. The book presents a unique overview on algorithmic, applicational, and systems aspects arising in the development of efficient parallel solutions to irregularly structured problems
4 editions published in 1998 in English and held by 77 WorldCat member libraries worldwide
This book constitutes the refereed proceedings of the 5th International Symposium on Solving Irregularly Structured Problems in Parallel, IRREGULAR'98, held in Berkeley, California, in August 1998. The 26 revised full papers presented were carefully reviewed and selected for inclusion from several dozen submissions. Also included are abstracts of four invited talks and 6 invited presentations given during minisymposia held in parallel. The book presents a unique overview on algorithmic, applicational, and systems aspects arising in the development of efficient parallel solutions to irregularly structured problems
Proceedings of the nineteenth annual ACMSIAM symposium on Discrete algorithms by
ShangHua Teng(
)
1 edition published in 2008 in English and held by 17 WorldCat member libraries worldwide
1 edition published in 2008 in English and held by 17 WorldCat member libraries worldwide
Probabilistic methods in the design and analysis of algorithms 07391 abstracts collection ; Dagstuhl seminar(
)
1 edition published in 2007 in English and held by 17 WorldCat member libraries worldwide
1 edition published in 2007 in English and held by 17 WorldCat member libraries worldwide
Proceedings of the nineteenth annual ACMSIAM symposium on Discrete algorithms by
ShangHua Teng(
)
1 edition published in 2008 in English and held by 11 WorldCat member libraries worldwide
1 edition published in 2008 in English and held by 11 WorldCat member libraries worldwide
Scalable algorithms for data and network analysis by
ShangHua Teng(
Book
)
3 editions published in 2016 in English and held by 10 WorldCat member libraries worldwide
In the age of Big Data, efficient algorithms are now in higher demand more than ever before. While Big Data takes us into the asymptotic world envisioned by our pioneers, it also challenges the classical notion of efficient algorithms: Algorithms that used to be considered efficient, according to polynomialtime characterization, may no longer be adequate for solving today's problems. It is not just desirable, but essential, that efficient algorithms should be scalable. In other words, their complexity should be nearly linear or sublinear with respect to the problem size. Thus, scalability, not just polynomialtime computability, should be elevated as the central complexity notion for characterizing efficient computation. In this tutorial, I will survey a family of algorithmic techniques for the design of provablygood scalable algorithms. These techniques include local network exploration, advanced sampling, sparsification, and geometric partitioning. They also include spectral graphtheoretical methods, such as those used for computing electrical flows and sampling from Gaussian Markov random fields. These methods exemplify the fusion of combinatorial, numerical, and statistical thinking in network analysis. I will illustrate the use of these techniques by a few basic problems that are fundamental in network analysis, particularly for the identification of significant nodes and coherent clusters/communities in social and information networks. I also take this opportunity to discuss some frameworks beyond graphtheoretical models for studying conceptual questions to understand multifaceted network data that arise in social influence, network dynamics, and Internet economics
3 editions published in 2016 in English and held by 10 WorldCat member libraries worldwide
In the age of Big Data, efficient algorithms are now in higher demand more than ever before. While Big Data takes us into the asymptotic world envisioned by our pioneers, it also challenges the classical notion of efficient algorithms: Algorithms that used to be considered efficient, according to polynomialtime characterization, may no longer be adequate for solving today's problems. It is not just desirable, but essential, that efficient algorithms should be scalable. In other words, their complexity should be nearly linear or sublinear with respect to the problem size. Thus, scalability, not just polynomialtime computability, should be elevated as the central complexity notion for characterizing efficient computation. In this tutorial, I will survey a family of algorithmic techniques for the design of provablygood scalable algorithms. These techniques include local network exploration, advanced sampling, sparsification, and geometric partitioning. They also include spectral graphtheoretical methods, such as those used for computing electrical flows and sampling from Gaussian Markov random fields. These methods exemplify the fusion of combinatorial, numerical, and statistical thinking in network analysis. I will illustrate the use of these techniques by a few basic problems that are fundamental in network analysis, particularly for the identification of significant nodes and coherent clusters/communities in social and information networks. I also take this opportunity to discuss some frameworks beyond graphtheoretical models for studying conceptual questions to understand multifaceted network data that arise in social influence, network dynamics, and Internet economics
Matching randomly in parallel by
ShangHua Teng(
Book
)
3 editions published in 1989 in English and held by 8 WorldCat member libraries worldwide
Abstract: "In this paper, the parallel complexity of the Random Matching Problema problem of generating a perfect matching in a bipartite graph uniformly in randomis considered. We show that the only known polynomial time random matching algorithm, due to Broder, Jerrum, and Sinclair, can not be parallelized in NC, unless NC = P. The reduction is from the Lexical First Maximal Independent Set Problem. This result shows many interesting structural properties between matching and lexical first maximal independent sets. It also leaves many interesting and important open questions. We also show that any polynomial time scheme (NC scheme) for the Random Maximal Independent Set Problem implies NP = RP (NP = RNC). This provides another example that the problem of uniform random generation is harder than the corresponding construction problem."
3 editions published in 1989 in English and held by 8 WorldCat member libraries worldwide
Abstract: "In this paper, the parallel complexity of the Random Matching Problema problem of generating a perfect matching in a bipartite graph uniformly in randomis considered. We show that the only known polynomial time random matching algorithm, due to Broder, Jerrum, and Sinclair, can not be parallelized in NC, unless NC = P. The reduction is from the Lexical First Maximal Independent Set Problem. This result shows many interesting structural properties between matching and lexical first maximal independent sets. It also leaves many interesting and important open questions. We also show that any polynomial time scheme (NC scheme) for the Random Maximal Independent Set Problem implies NP = RP (NP = RNC). This provides another example that the problem of uniform random generation is harder than the corresponding construction problem."
Points, spheres, and separators : a unified geometric approach to graph partitioning by
ShangHua Teng(
Book
)
2 editions published in 1991 in English and held by 8 WorldCat member libraries worldwide
2 editions published in 1991 in English and held by 8 WorldCat member libraries worldwide
Spectral partitioning works : planar graphs and finite element meshes by Daniel A Spielman(
Book
)
1 edition published in 1996 in English and held by 5 WorldCat member libraries worldwide
Abstract: "Spectral partitioning methods use the Fiedler vector   the eigenvector of the secondsmallest eigenvalue of the Laplacian matrix  to find a small separator of a graph. These methods are important components of many scientific numerical algorithms and have been demonstrated by experiment to work extremely well. In this paper, we show that spectral partitioning methods work well on boundeddegree planar graphs and finite element meshes  the classes of graphs to which they are usually applied. While naive spectral bisection does not necessarily work, we prove that spectral partitioning techniques can be used to produce separators whose ratio of vertices removed to edges cut is O([square root of n]) for boundeddegree planar graphs and twodimensional meshes and O(n[superscript 1/d]) for wellshaped ddimensional meshes. The heart of our analysis is an upper bound on the secondsmallest eigenvalues of the Laplacian matrices of these graphs."
1 edition published in 1996 in English and held by 5 WorldCat member libraries worldwide
Abstract: "Spectral partitioning methods use the Fiedler vector   the eigenvector of the secondsmallest eigenvalue of the Laplacian matrix  to find a small separator of a graph. These methods are important components of many scientific numerical algorithms and have been demonstrated by experiment to work extremely well. In this paper, we show that spectral partitioning methods work well on boundeddegree planar graphs and finite element meshes  the classes of graphs to which they are usually applied. While naive spectral bisection does not necessarily work, we prove that spectral partitioning techniques can be used to produce separators whose ratio of vertices removed to edges cut is O([square root of n]) for boundeddegree planar graphs and twodimensional meshes and O(n[superscript 1/d]) for wellshaped ddimensional meshes. The heart of our analysis is an upper bound on the secondsmallest eigenvalues of the Laplacian matrices of these graphs."
Space efficient processor identity protocols by
ShangHua Teng(
Book
)
2 editions published in 1989 in English and held by 5 WorldCat member libraries worldwide
2 editions published in 1989 in English and held by 5 WorldCat member libraries worldwide
Functional inversion and communication complexity by
ShangHua Teng(
Book
)
3 editions published in 1992 in English and held by 4 WorldCat member libraries worldwide
Abstract: "In this paper, we study the relation between the multiparty communication complexity over various communication topologies and the complexity of inverting functions and/or permutations. In particular, we show that if a function has a ringprotocol or a tree protocol of communication complexity bounded by [symbol], then there is a circuit of size 2[superscript O([symbol])]n computing an inverse of the function. Consequently, we have proved, although inverting NC⁰ Boolean circuits is NPcomplete, planar NC¹ Boolean circuits can be inverted in NC, and hence in polynomial time. In general, NC[superscript k] planar boolean circuits can be inverted in O(n[superscript log[superscript(k1)]n) time. Also from the ringprotocol result, we derive an [omega](n log n) lower bound on the VLSI area to layout any oneway function. Our results on inverting boolean circuits can be extended to algebraic circuits over finite rings. One significant aspect of these results is that they enable us to compare the communication power of two topologies. We have proved that on some topologies, no oneway function nor its inverse can be computed with a bounded communication complexity."
3 editions published in 1992 in English and held by 4 WorldCat member libraries worldwide
Abstract: "In this paper, we study the relation between the multiparty communication complexity over various communication topologies and the complexity of inverting functions and/or permutations. In particular, we show that if a function has a ringprotocol or a tree protocol of communication complexity bounded by [symbol], then there is a circuit of size 2[superscript O([symbol])]n computing an inverse of the function. Consequently, we have proved, although inverting NC⁰ Boolean circuits is NPcomplete, planar NC¹ Boolean circuits can be inverted in NC, and hence in polynomial time. In general, NC[superscript k] planar boolean circuits can be inverted in O(n[superscript log[superscript(k1)]n) time. Also from the ringprotocol result, we derive an [omega](n log n) lower bound on the VLSI area to layout any oneway function. Our results on inverting boolean circuits can be extended to algebraic circuits over finite rings. One significant aspect of these results is that they enable us to compare the communication power of two topologies. We have proved that on some topologies, no oneway function nor its inverse can be computed with a bounded communication complexity."
Geometric spectral partitioning by
Tony F Chan(
Book
)
3 editions published between 1994 and 1995 in English and held by 4 WorldCat member libraries worldwide
Abstract: "We investigate a new method for partitioning a graph into two equalsized pieces with few connecting edges. We combine ideas from two recently suggested partitioning algorithms, spectral bisection (which uses an eigenvector of a matrix associated with the graph) and geometric bisection (which applies to graphs that are meshes in Euclidean space). The new method does not require geometric coordinates, and it produces partitions that are often better than either the spectral or geometric ones."
3 editions published between 1994 and 1995 in English and held by 4 WorldCat member libraries worldwide
Abstract: "We investigate a new method for partitioning a graph into two equalsized pieces with few connecting edges. We combine ideas from two recently suggested partitioning algorithms, spectral bisection (which uses an eigenvector of a matrix associated with the graph) and geometric bisection (which applies to graphs that are meshes in Euclidean space). The new method does not require geometric coordinates, and it produces partitions that are often better than either the spectral or geometric ones."
ACM Symposium on Parallel Algorithms and Architectures : [archival versions of working papers presented at the Twelfth ACM
Symposium ..., July 912, 2000 at Bar Harbor, Maine] by
Symposium on Parallel Algorithms and Architectures(
Book
)
2 editions published in 2002 in English and held by 4 WorldCat member libraries worldwide
2 editions published in 2002 in English and held by 4 WorldCat member libraries worldwide
Geometric mesh partitioning : implementation and experiments by
J. R Gilbert(
Book
)
3 editions published in 1994 in English and held by 4 WorldCat member libraries worldwide
Abstract: "We investigate a method of dividing an irregular mesh into equalsized pieces with few interconnecting edges. The method's novel feature is that it exploits the geometric coordinates of the mesh vertices. It is based on theoretical work of Miller, Teng, Thurston, and Vavasis, who showed that certain classes of 'wellshaped' finite element meshes have good separators. The geometric method is quite simple to implement : we describe a Matlab code for it in some detail. The method is also quite efficient and effective: we compare it with some other methods, including spectral bisection."
3 editions published in 1994 in English and held by 4 WorldCat member libraries worldwide
Abstract: "We investigate a method of dividing an irregular mesh into equalsized pieces with few interconnecting edges. The method's novel feature is that it exploits the geometric coordinates of the mesh vertices. It is based on theoretical work of Miller, Teng, Thurston, and Vavasis, who showed that certain classes of 'wellshaped' finite element meshes have good separators. The geometric method is quite simple to implement : we describe a Matlab code for it in some detail. The method is also quite efficient and effective: we compare it with some other methods, including spectral bisection."
A geometric approach to parallel hierarchical and adaptive computing on unstructured meshes by
ShangHua Teng(
Book
)
2 editions published in 1994 in English and held by 3 WorldCat member libraries worldwide
Abstract: "The use of wellshaped unstructured meshes is essential for three dimensional applications with complex geometries or whose solution changes rapidly. Computationally, both hierarchical and adaptive methods perform an iterative computation over a series of unstructured meshes and use interpolation or restriction to transform partial solutions from mesh to mesh. The effectiveness of parallel hierarchical and adaptive computing rely on an efficient and scalable parallel solution to a set of key algorithmic problems such as mesh generation, graph partitioning, mesh coarsening, adaptive refinement, unstructured interpolation, sparse linear system solving and many other problems that they subsequently creat [sic]. This paper proposes a unified approach to solve these problems simultaneously. Our approach exploits the geometric structure of the problem and has application to multigrid (MG) and domain decomposition (DD) on unstructured meshes. Its kernel is the geometric mesh partitioner developed by Miller, Teng, Thurston and Vavasis. Our 3D algorithm has the same simplicity as a 2D algorithm."
2 editions published in 1994 in English and held by 3 WorldCat member libraries worldwide
Abstract: "The use of wellshaped unstructured meshes is essential for three dimensional applications with complex geometries or whose solution changes rapidly. Computationally, both hierarchical and adaptive methods perform an iterative computation over a series of unstructured meshes and use interpolation or restriction to transform partial solutions from mesh to mesh. The effectiveness of parallel hierarchical and adaptive computing rely on an efficient and scalable parallel solution to a set of key algorithmic problems such as mesh generation, graph partitioning, mesh coarsening, adaptive refinement, unstructured interpolation, sparse linear system solving and many other problems that they subsequently creat [sic]. This paper proposes a unified approach to solve these problems simultaneously. Our approach exploits the geometric structure of the problem and has application to multigrid (MG) and domain decomposition (DD) on unstructured meshes. Its kernel is the geometric mesh partitioner developed by Miller, Teng, Thurston and Vavasis. Our 3D algorithm has the same simplicity as a 2D algorithm."
Parallel construction of quadtrees and quality triangulations by
Marshall Wayne Bern(
Book
)
2 editions published in 1994 in English and held by 3 WorldCat member libraries worldwide
Abstract: "We describe efficient PRAM algorithms for constructing unbalanced quadtrees, balanced quadtrees, and quadtreebased finite element meshes. Our algorithms take time O(log n) for point set input and O(log n log k) time for planar straightline graphs, using O(n+k/log n) processors, where n measures input size k output size."
2 editions published in 1994 in English and held by 3 WorldCat member libraries worldwide
Abstract: "We describe efficient PRAM algorithms for constructing unbalanced quadtrees, balanced quadtrees, and quadtreebased finite element meshes. Our algorithms take time O(log n) for point set input and O(log n log k) time for planar straightline graphs, using O(n+k/log n) processors, where n measures input size k output size."
Combinational aspects of geometric graphs by
ShangHua Teng(
Book
)
2 editions published in 1994 in English and held by 3 WorldCat member libraries worldwide
Abstract: "As a special case of our main result, we show that for all L> 0, each knearest neighborhood graph in d dimensions excludes K[subscript h] as a depth L minor if h = [omega](L[superscript d1]). More generally, we prove that the overlap graphs defined by Miller, Teng, Thurston and Vavasis [18] have this combinatorial property. By a construction of Plotkin, Rao and Smith [23], our result implies that overlap graphs have 'good' cutcovers, answering an open question of Kaklamanis, Krizanc and Rao [12]. Consequently, overlap graphs can be emulated on hypercube graphs with a constant factor of slowdown and on butterfly graphs with a factor of 0(log* n) slowdown. Therefore, computations on overlap graphs, such as finiteelement and finite difference methods on 'wellconditioned' meshes and image processing on k nearest neighborhood graphs, can be performed on hypercubic parallel machines with linear speedup. Our result, in conjunction with a result of Plotkin, Rao and Smith, also yields a combinatorial proof to that overlap graphs have separators of sublinear size. We also show that with high probability, the Delaunay diagram, the relative neighborhood graph and the knearest neighborhood graph of a random point set exclude K[subscript h] as a depth L minor if h = [omega](L[superscript d/2] log n)."
2 editions published in 1994 in English and held by 3 WorldCat member libraries worldwide
Abstract: "As a special case of our main result, we show that for all L> 0, each knearest neighborhood graph in d dimensions excludes K[subscript h] as a depth L minor if h = [omega](L[superscript d1]). More generally, we prove that the overlap graphs defined by Miller, Teng, Thurston and Vavasis [18] have this combinatorial property. By a construction of Plotkin, Rao and Smith [23], our result implies that overlap graphs have 'good' cutcovers, answering an open question of Kaklamanis, Krizanc and Rao [12]. Consequently, overlap graphs can be emulated on hypercube graphs with a constant factor of slowdown and on butterfly graphs with a factor of 0(log* n) slowdown. Therefore, computations on overlap graphs, such as finiteelement and finite difference methods on 'wellconditioned' meshes and image processing on k nearest neighborhood graphs, can be performed on hypercubic parallel machines with linear speedup. Our result, in conjunction with a result of Plotkin, Rao and Smith, also yields a combinatorial proof to that overlap graphs have separators of sublinear size. We also show that with high probability, the Delaunay diagram, the relative neighborhood graph and the knearest neighborhood graph of a random point set exclude K[subscript h] as a depth L minor if h = [omega](L[superscript d/2] log n)."
Algorithms and Computation: Proceedings of the 11th International Conference, ISAAC 2000, Taipei, Taiwan, December 1820,
2000 by DerTsai Lee(
Book
)
2 editions published between 2000 and 2001 in English and held by 3 WorldCat member libraries worldwide
The papers in this volume were selected for presentation at the Eleventh Annual International Symposium on Algorithms and Computation (ISAAC 2000), held on 18{20 December, 2000 at the Institute of Information Science, Academia Sinica, Taipei, Taiwan. Previous meetings were held in Tokyo (1990), Taipei (1991), Nagoya (1992), Hong Kong (1993), Beijing (1994), Cairns (1995), Osaka (1996), Singapore (1997), Taejon (1998), and Chennai (1999). Submissions to the conference this year were conducted entirely electro cally. Thanks to the excellent software developed by the Institute of Information Science, Academia Sinica, we were able to carry out virtually all communication via the World Wide Web. In response to the call for papers, a total of 87 extended abstracts were submitted from 25 countries. Each submitted paper was handled by at least three program committee members, with the assistance of a number of external reviewers, as indicated by the referee list found in the proceedings. There were many more acceptable papers than there was space available in the symposium program, which made the program committee{u2019}s task extremely di cult. Finally 46 papers were selected for presentation at the Symposium. In addition to these contributed papers, the conference also included two invited presentations by Dr. JeanDaniel Boissonnat, INRIA SophiaAntipolis, France and Professor JinYi Cai, University of Wisconsin at Madison, Wisconsin, USA. It is expected that most of the accepted papers will appear in a more complete form in scienti c journals
2 editions published between 2000 and 2001 in English and held by 3 WorldCat member libraries worldwide
The papers in this volume were selected for presentation at the Eleventh Annual International Symposium on Algorithms and Computation (ISAAC 2000), held on 18{20 December, 2000 at the Institute of Information Science, Academia Sinica, Taipei, Taiwan. Previous meetings were held in Tokyo (1990), Taipei (1991), Nagoya (1992), Hong Kong (1993), Beijing (1994), Cairns (1995), Osaka (1996), Singapore (1997), Taejon (1998), and Chennai (1999). Submissions to the conference this year were conducted entirely electro cally. Thanks to the excellent software developed by the Institute of Information Science, Academia Sinica, we were able to carry out virtually all communication via the World Wide Web. In response to the call for papers, a total of 87 extended abstracts were submitted from 25 countries. Each submitted paper was handled by at least three program committee members, with the assistance of a number of external reviewers, as indicated by the referee list found in the proceedings. There were many more acceptable papers than there was space available in the symposium program, which made the program committee{u2019}s task extremely di cult. Finally 46 papers were selected for presentation at the Symposium. In addition to these contributed papers, the conference also included two invited presentations by Dr. JeanDaniel Boissonnat, INRIA SophiaAntipolis, France and Professor JinYi Cai, University of Wisconsin at Madison, Wisconsin, USA. It is expected that most of the accepted papers will appear in a more complete form in scienti c journals
A deterministic linear time algorithm for geometric separators and its application by
David Eppstein(
Book
)
2 editions published in 1994 in English and held by 3 WorldCat member libraries worldwide
Abstract: "We give a deterministic linear time algorithm for finding a 'good' sphere separator of a kply neighborhood system [phi] in any fixed dimension, where a kply neighborhood system in R[superscript d] is a collection of n balls such that no points in the space is covered by more than k balls. The separating sphere intersects at most O(k[superscript 1/d]n[superscript 11/d] balls of [phi] and divides the remaining of [phi] into two parts: those in the interior and those in the exterior of the sphere, respectively, so that the larger part contains at most [delta]n balls ((d+1)/(d+2)<[delta]<1). This result improves the O(n²) time deterministic algorithm of Miller and Teng [30] and answers a major algorithmic open question posed by Miller, Teng, Thurston, and Vavasis [23, 26]. The deterministic algorithm hinges on the use of a new method for deriving the separator property of neighborhood systems. Using this algorithm, we devise an O(kn+n log n) time deterministic algorithm for computing the intersection graph of a kply neighborhood system. We give an O(n log n) time algorithm for constructing a linear space, O(log n) query time search structure for a geometric query problem associated with kply neighborhood systems, and we use this data structure in an algorithm for approximating the value of k within a constant factor in time O(n log n). We also develop a deterministic linear time algorithm for finding an O(k[superscript 1/d]n[superscript 11/d])separator for a knearest neighborhood graph in d dimensions."
2 editions published in 1994 in English and held by 3 WorldCat member libraries worldwide
Abstract: "We give a deterministic linear time algorithm for finding a 'good' sphere separator of a kply neighborhood system [phi] in any fixed dimension, where a kply neighborhood system in R[superscript d] is a collection of n balls such that no points in the space is covered by more than k balls. The separating sphere intersects at most O(k[superscript 1/d]n[superscript 11/d] balls of [phi] and divides the remaining of [phi] into two parts: those in the interior and those in the exterior of the sphere, respectively, so that the larger part contains at most [delta]n balls ((d+1)/(d+2)<[delta]<1). This result improves the O(n²) time deterministic algorithm of Miller and Teng [30] and answers a major algorithmic open question posed by Miller, Teng, Thurston, and Vavasis [23, 26]. The deterministic algorithm hinges on the use of a new method for deriving the separator property of neighborhood systems. Using this algorithm, we devise an O(kn+n log n) time deterministic algorithm for computing the intersection graph of a kply neighborhood system. We give an O(n log n) time algorithm for constructing a linear space, O(log n) query time search structure for a geometric query problem associated with kply neighborhood systems, and we use this data structure in an algorithm for approximating the value of k within a constant factor in time O(n log n). We also develop a deterministic linear time algorithm for finding an O(k[superscript 1/d]n[superscript 11/d])separator for a knearest neighborhood graph in d dimensions."
Moments of inertia and graph separators by K Gramban(
Book
)
2 editions published in 1994 in English and held by 3 WorldCat member libraries worldwide
Abstract: "Graphs that arise from the finite element or finite difference methods often include geometric information such as the coordinates of the nodes of the graph. The geometric separator algorithm of Miller, Teng, Thurston, and Vavasis uses some of the available geometric information to find small node separators of graphs. The algorithm utilizes a random sampling technique based on the uniform distribution to find a good separator given an approximate graph center point. In this paper, we show that sampling from an ellipsoidal distribution based on the inertia matrix of the graph can significantly improve the quality of the separator. More generally, we show that, given a cost function f on the unit dsphere U[subscript d], we can define an ellipsoidal distribution based on the second moments of f, and that the expectation of f with respect to the ellipsoidal distribution is, in almost all cases, less than the expectation with respect to the uniform distribution. We also present experimental results that demonstrate the significant benefit gained by use of the additional geometric information. Some previous algorithms have used the moments of inertia heuristically, and suffer from extremely poor worst case performance. This is the first result, to our knowledge, that incorporates the moments of inertia into a provably good strategy."
2 editions published in 1994 in English and held by 3 WorldCat member libraries worldwide
Abstract: "Graphs that arise from the finite element or finite difference methods often include geometric information such as the coordinates of the nodes of the graph. The geometric separator algorithm of Miller, Teng, Thurston, and Vavasis uses some of the available geometric information to find small node separators of graphs. The algorithm utilizes a random sampling technique based on the uniform distribution to find a good separator given an approximate graph center point. In this paper, we show that sampling from an ellipsoidal distribution based on the inertia matrix of the graph can significantly improve the quality of the separator. More generally, we show that, given a cost function f on the unit dsphere U[subscript d], we can define an ellipsoidal distribution based on the second moments of f, and that the expectation of f with respect to the ellipsoidal distribution is, in almost all cases, less than the expectation with respect to the uniform distribution. We also present experimental results that demonstrate the significant benefit gained by use of the additional geometric information. Some previous algorithms have used the moments of inertia heuristically, and suffer from extremely poor worst case performance. This is the first result, to our knowledge, that incorporates the moments of inertia into a provably good strategy."
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Algorithms Big data Combinatorial geometry Computational complexity Computer algorithms Computer graphics Computer networks Computer networksScalability Computer programming Computers Computer science Computer scienceMathematics Computer software Cryptography Data structures (Computer science) Electronic data processing Electronic data processingDistributed processing Finite element method GeometryData processing Graph theory Linear systems Mathematical analysis Nets (Mathematics) Numerical calculationsData processing Online algorithms Parallel processing (Electronic computers) Partitions (Mathematics) ScienceData processing Sparse matrices Spectral theory (Mathematics)
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ShangHua Teng ChineseAmerican computer scientist (b.1964)
ShangHua Teng chinesischer Informatiker
ShangHua Teng wiskundige uit China
Teng, S.H.
滕尚华 中国计算机科学家
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