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

2011
*
Lecture Notes in Computer Science
*

We address this problem with

doi:10.1007/978-3-642-20847-8_2
fatcat:owpg3prm6ramdfjll74dlhmzxy
*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

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]

2010
*
Lecture Notes in Computer Science
*

Select

doi:10.1007/978-3-642-11409-0_1
fatcat:rqrljmkgqrb3ddw5nszva6ighi
*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

2014
*
IEEE Transactions on Knowledge and Data Engineering
*

We address this problem with

doi:10.1109/tkde.2012.244
fatcat:sxogvibd7rb5roa55uhke5pbfa
*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

2005
*
SIAM journal on computing (Print)
*

We prove

doi:10.1137/s0097539703434267
fatcat:2ozdkdafgzcxbanveap6izyafu
*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]

2005
*
arXiv
*
pre-print

We prove

arXiv:cs/0309014v2
fatcat:aflnbpfryzddrhhfkrwus34a3m
*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 program to be executed

doi:10.1145/77726.255144
dblp:conf/ics/HoustisRCKPSVWW90
fatcat:h5wr3y2xifh3pfeenkupixe24u
*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

2008
*
Proceedings of the twentieth annual symposium on Parallelism in algorithms and architectures - SPAA '08
*

We show how these

doi:10.1145/1378533.1378559
dblp:conf/spaa/KoutisM08
fatcat:m2adbqdzcjeanmhijyrtbou5ga
*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]

2009
*
arXiv
*
pre-print

Often,

arXiv:0908.3916v1
fatcat:s4kizimp7jggliyivcqm5iokmm
*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

doi:10.1016/0898-1221(93)90188-2
fatcat:paoxxhotcbagbfrmenudtpn2ea
*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

2001
*
International journal of computational geometry and applications
*

Terrain polyhedra have a base facet such that, for each point of

doi:10.1142/s0218195901000687
fatcat:42n4mkhzergodofmietzrfgvle
*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]

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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