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### Spectral Analysis for Billion-Scale Graphs: Discoveries and Implementation [chapter]

U Kang, Brendan Meeder, Christos Faloutsos
2011 Lecture Notes in Computer Science
We address this problem with the proposed HEIGEN algorithm, which we carefully design to be accurate, efficient, and able to run on the highly scalable MAPRE-DUCE (HADOOP) environment.  ...  We report important discoveries about near-cliques and triangles on several real-world graphs, including a snapshot of the Twitter social network (38Gb, 2 billion edges) and the "YahooWeb" dataset, one  ...  Acknowledgements This material is based upon work supported by the National Science  ...

### Combinatorial algorithms enabling computational science: tales from the front

Sanjukta Bhowmick, Erik G Boman, Karen Devine, Assefaw Gebremedhin, Bruce Hendrickson, Paul Hovland, Todd Munson, Alex Pothen
2006 Journal of Physics, Conference Series
The importance of discrete algorithms continues to grow with the demands of new applications and advanced architectures.  ...  Combinatorial algorithms have long played a crucial enabling role in scientific and engineering computations.  ...  The most common matrix distribution is a one-dimensional (1D) decomposition of either matrix rows or columns.  ...

### Graph-Theoretic Solutions to Computational Geometry Problems [chapter]

David Eppstein
2010 Lecture Notes in Computer Science
Select the vertices with the least-frequently-used color The points within any triangle can be seen from the triangle vertex of the selected color Algorithmic implications Graph coloring is hard in general  ...  Lapok 1931] In a bipartite graph, independence number = n -|M| where M is a maximum matching Upper bound: For arbitrary graphs, # MIS ≤ # vertices -# match (MIS can only use one vertex from  ...  , distortion = max dilation Conclusions Graph-theoretic point of view is useful in many non-graph problems The graph algorithms used for these problems are often classical... maximum independent set  ...

### Page 4107 of Mathematical Reviews Vol. , Issue 98G [page]

1998 Mathematical Reviews
G. (1-ABRN-DS; Auburn, Al The intersection problem for star designs.  ...  Probably half a dozen times in the last several years I have come across a problem in design theory (or a graph decomposition problem) where substantial progress could have been made had one been able  ...

### HEigen: Spectral Analysis for Billion-Scale Graphs

U Kang, Brendan Meeder, Evangelos E. Papalexakis, Christos Faloutsos
2014 IEEE Transactions on Knowledge and Data Engineering
We address this problem with the proposed HEIGEN algorithm, which we carefully design to be accurate, efficient and able to run on the highly scalable MAPREDUCE (HADOOP) environment.  ...  We report important discoveries about near-cliques and triangles on several real-world graphs, including a snapshot of the Twitter social network (56Gb, 2 billion edges) and the "YahooWeb" dataset, one  ...  The U.S. Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation here on.  ...

### Optimal Covering Tours with Turn Costs

Esther M. Arkin, Michael A. Bender, Erik D. Demaine, Sándor P. Fekete, Joseph S. B. Mitchell, Saurabh Sethia
2005 SIAM journal on computing (Print)
We prove the NP-completeness of minimum-turn milling and give efficient approximation algorithms for several natural versions of the problem, including a polynomialtime approximation scheme based on a  ...  ("pocket") in order to minimize a cost that depends mainly on the number of turns.  ...  We are obliged to Valentin Polishchuk for a very thorough list of suggestions, and thank three anonymous referees for various comments that helped to improve the presentation of the paper.  ...

### Optimal Covering Tours with Turn Costs [article]

Esther M. Arkin, Michael A. Bender, Erik D. Demaine, Sandor P. Fekete, Joseph S. B. Mitchell, Saurabh Sethia
2005 arXiv   pre-print
We prove the NP-completeness of minimum-turn milling and give efficient approximation algorithms for several natural versions of the problem, including a polynomial-time approximation scheme based on a  ...  ("pocket"), in order to minimize a cost that depends mainly on the number of em turns.  ...  We are obliged to Valentin Polishchuk for a very thorough list of suggestions, and thank three anonymous referees for various comments that helped to improve the presentation of the paper.  ...

### //ELLPACK

E. N. Houstis, J. R. Rice, N. P. Chrisochoides, H. C. Karathanasis, P. N. Papachiou, M. K. Samartzis, E. A. Vavalis, Ko Yang Wang, S. Weerawarana
1990 Proceedings of the 4th international conference on Supercomputing - ICS '90
. / /ELLPACK program to be executed on a four processor NCUBE machine using domain decomposition, 5-point star discretization, and a Jacobi 51 iteration method.  ...  In this section we describe the design of a PDE solving system capable of supporting the parallel processing of elliptic PDEs on MIMD machines and which incorporates many of the facets of the next generation  ...  The 3-D data visualization tool can be used to visualize any data structures or functions on the 3-D domains including the decomposition and mapping of 3-D domains and the 3-D meshes. 22  ...

### Graph partitioning into isolated, high conductance clusters

Ioannis Koutis, Gary L. Miller
2008 Proceedings of the twentieth annual symposium on Parallelism in algorithms and architectures - SPAA '08
We show how these decompositions can be used in the first known linear work parallel construction of provably good preconditioners for the important class of fixed degree graph Laplacians.  ...  We show that for planar graphs we can compute a decomposition P such that |P | < n/ρ, where ρ is a constant, in O(log n) parallel time with O(n) work.  ...  The computation of the 3-critical vertices can be done with linear work in O(log n) parallel time using the parallel tree contraction algorithms [26] .  ...

### Graph-Theoretic Solutions to Computational Geometry Problems [article]

David Eppstein
2009 arXiv   pre-print
Often, the efficiency of the algorithm depends on the special properties of the graph constructed in this way.  ...  Many problems in computational geometry are not stated in graph-theoretic terms, but can be solved efficiently by constructing an auxiliary graph and performing a graph-theoretic algorithm on it.  ...  Acknowledgements This work was supported in part by NSF grant 0830403 and by the Office of Naval Research under grant N00014-08-1-1015.  ...

### Page 1206 of Mathematical Reviews Vol. , Issue 97B [page]

1997 Mathematical Reviews
The n-star graph is a recently introduced interconnection net- work for massively parallel systems.  ...  Embedding binary trees into another network—the host network—helps in designing solutions for the host network using the known solutions on binary trees.  ...

### Page 4339 of Mathematical Reviews Vol. , Issue 2000f [page]

2000 Mathematical Reviews
Liu and Xuding Zhu, Star-extremal circulant graphs (301-309); Laxmi Parida, On the approximability of physical map problems using single mole- cule methods (extended abstract) (310-328); Arno Schénegge  ...  The singular value decomposition is applied to compute the orthogonal projector and its Fréchet derivative.  ...

### Topological properties of star graphs

1993 Computers and Mathematics with Applications
They can also be readily utilized to design routing algorithms and to compute contention and traffic congestion in networks that use star graphs as the underlying topology.  ...  Our purpose in the present paper is to investigate different topological properties of the recently introduced star graphs which are being viewed as attractive alternatives to n-cubes or hypercubes.  ...  as well as of mapping parallel algorithms on the networks.  ...

### TERRAIN DECOMPOSITION AND LAYERED MANUFACTURING

SÁNDOR P. FEKETE, JOSEPH S. B. MITCHELL
2001 International journal of computational geometry and applications
Terrain polyhedra have a base facet such that, for each point of the polyhedron, the line segment joining the point to its orthogonal projection on the base facet lies within the polyhedron.  ...  Terrain polyhedra are exactly the class of polyhedral models for which it is possible to construct the model using layered manufacturing (with layers parallel to the base facet), without the need for constructing  ...  Acknowledgments We are most grateful to Godfried Toussaint for useful discussions on these problems, help in formulating the problem, and organizing the 1993 Barbados Workshop on Geometric and Computational  ...

### Convex Optimization for Parallel Energy Minimization [article]

K. S. Sesh Kumar, Alvaro Barbero, Stefanie Jegelka, Francis Bach (LIENS,INRIA Paris - Rocquencourt)
2015 arXiv   pre-print
On small problems the iterative convex methods match the combinatorial max-flow algorithms, while on larger problems they offer other flexibility and important gains: (a) their memory footprint is small  ...  With growing image sizes (2D and 3D), it is now highly desirable to run energy minimization algorithms in parallel.  ...  The convex algorithms admit stochastic variants too [15] . However, the decompositions used in the experiments here (Figure 1 ) only use a decomposition into 2-4 functions.  ...
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