Article

Multilevel algorithms for partitioning power-law graphs

Authors:

Amine Abou-Rjeili,

George KarypisAuthors Info & Claims

IPDPS'06: Proceedings of the 20th international conference on Parallel and distributed processing

Page 124

Published: 25 April 2006 Publication History

Abstract

Graph partitioning is an enabling technology for parallel processing as it allows for the effective decomposition of unstructured computations whose data dependencies correspond to a large sparse and irregular graph. Even though the problem of computing high-quality partitionings of graphs arising in scientific computations is to a large extent well-understood, this is far from being true for emerging HPC applications whose underlying computation involves graphs whose degree distribution follows a powerlaw curve. This paper presents new multilevel graph partitioning algorithms that are specifically designed for partitioning such graphs. It presents new clustering-based coarsening schemes that identify and collapse together groups of vertices that are highly connected. An experimental evaluation of these schemes on 10 different graphs show that the proposed algorithms consistently and significantly outperform existing state-of-the-art approaches.

References

[1]

C. Ashcraft and J. Liu. Using domain decomposition to find graph bisectors. Technical report, York University, North York, Ontario, Canada, 1995.

[2]

T. Bui and C. Jones. A heuristic for reducing fill in sparse matrix factorization. In 6th SIAM Conf. Parallel Processing for Scientific Computing, pages 445-452, 1993.

[3]

U. Catalyurek and C. Aykanat. Hypergraph-partitioning based decomposition for parallel sparse-matrix vector multiplication. IEEE Transactions on Parallel and Distributed Systems, 10(7):673-693, 1999.

Digital Library

[4]

J. Cong and M. L. Smith. A parallel bottom-up clustering algorithm with applications to circuit partitioning in vlsi design. In Proc. ACM/IEEE Design Automation Conference, pages 755-760, 1993.

Digital Library

[5]

R. Diekmann, B. Monien, and R. Preis. Using helpful sets to improve graph bisections. In D. Hsu, A. Rosenberg, and D. Sotteau, editors, Interconnection Networks and Mapping and Scheduling Parallel Computations, volume 21, pages 57-73. AMS Publications, DIMACS Volume Series, 1995.

[6]

R.O. Duda, P.E. Hart, and D.G. Stork. Pattern Classification. John Wiley & Sons, 2001.

Digital Library

[7]

C. M. Fiduccia and R. M. Mattheyses. A linear time heuristic for improving network partitions. In In Proc. 19th IEEE Design Automation Conference, pages 175-181, 1982.

Digital Library

[8]

H. Gabow. Data structures for weighted matching and nearest common ancestors with linking. In Proc. of the 1st Annual ACM-SIAM Symposium on Discrete Algorithms, pages 434-443, 1990.

Digital Library

[9]

Ananth Grama, Anshul Gupta, George Karypis, and Vipin Kumar. Introduction to Parallel Computing: Design and Analysis of Algorithms, 2nd Edition. Adison Wesley Publishing Company, Redwood City, CA, 2003.

[10]

W. Hager, S. Park, and T. Davis. Block exchange in graph partitioning. In P. Pardalos, editor, Approximation and Complexity in Numerical Optimization: Continuous and Discrete Problems. Kluwer Academic Publishers, 1999.

[11]

S. Hauck and G. Borriello. An evaluation of bipartitioning technique. In Proc. Chapel Hill Conference on Advanced Research in VLSI, 1995.

Digital Library

[12]

B. Hendrickson. Graph partitioning and parallel solvers: Has the emperor no clothes? In Proc. Irregular'98, pages 218- 225, 1998.

Digital Library

[13]

Bruce Hendrickson and Robert Leland. A multilevel algorithm for partitioning graphs. Technical Report SAND93- 1301, Sandia National Laboratories, 1993.

[14]

Bruce Hendrickson and Robert Leland. The chaco user's guide, version 2.0. Technical Report SAND94-2692, Sandia National Laboratories, 1994.

[15]

G. Karypis and V. Kumar. Analysis of multilevel graph partitioning. In Proceedings of Supercomputing, 1995.

Digital Library

[16]

G. Karypis and V. Kumar. Technical report, Department of Computer Science, University of Minnesota, 1998.

[17]

G. Karypis and V. Kumar. A fast and high quality multilevel scheme for partitioning irregular graphs. SIAM Journal on Scientific Computing, 20(1):359-392, 1998.

Digital Library

[18]

G. Karypis and V. Kumar. Multilevel k-way partitioning scheme for irregular graphs. Journal of Parallel and Distributed Computing, 48(1):96-129, 1998.

Digital Library

[19]

G. Karypis and V. Kumar. A fast and highly quality multilevel scheme for partitioning irregular graphs. SIAM Journal on Scientific Computing, 20(1), 1999.

Digital Library

[20]

B.W. Kernighan and S. Lin. An efficient heuristic procedure for partitioning graphs. The Bell System Technical Journal, 49(2):291-307, 1970.

[21]

J. Kleinberg. Authoritative sources in a hyperlinked environment. In Proc. of the Nineth Annual ACM-SIAM Symposium on Discrete Algorithms, 1998.

Digital Library

[22]

R. Tanaka J.C. Doyle W. Willinger L. Li, D. Alderson. Towards a theory of scale-free graphs: Definition, properties, and implications. Technical Report CIT-CDS-04-006, California Institute of Technology, Pasadena, CA, 2004.

[23]

R. Motwani T. Winograd L. Page, S. Brin. The pagerank citation ranking: Bringing order to the web. Technical report, Stanford Digital Library Technologies Project, 1998.

[24]

B. Monien, R. Preis, and R. Diekmann. Quality matching and local improvement for multilevel graph-partitioning. Technical report, University of Paderborn, 1999.

[25]

F. Pellegrini and J. Roman. SCOTCH: A software package for static mapping by dual recursive bipartitioning of process and architecture graphs. HPCN-Europe, Springer LNCS 1067, pages 493-498, 1996.

Digital Library

[26]

Seidman S.B. Network structure and minimum degree. Social Networks, 5:269-287, 1983.

[27]

Kirk Schloegel, George Karypis, and Vipin Kumar. Graph partitioning for high-performance scientific simulations. In Jack Dongara, Ian Foster, Geoffrey Fox, William Gropp, Ken Kennedy, Linda Torczon, and Andy White, editors, Source-book on Parallel Computing, chapter 18, pages 491-541. Morgan Kaufmann, San Francisco, CA, 2002.

Digital Library

[28]

M. Zaveršnik V. Batagelj. An O(m) algorithm for cores decomposition of networks.

[29]

M. Zaveršnik V. Batagelj. Generalized cores. Journal of the ACM, V(N):1-8, 2002.

Cited By

Agarwal SDutta SBhattacharya A(2020)ChiSeLProceedings of the VLDB Endowment10.14778/3401960.340196413:10(1654-1668)Online publication date: 1-Jun-2020
https://dl.acm.org/doi/10.14778/3401960.3401964
Lakhotia KKannan RPati SPrasanna V(2020)GPOPACM Transactions on Parallel Computing10.1145/33809427:1(1-24)Online publication date: 9-Mar-2020
https://dl.acm.org/doi/10.1145/3380942
Kolokasis IPratikakis P(2019)Cut to FitProceedings of the 2nd Joint International Workshop on Graph Data Management Experiences & Systems (GRADES) and Network Data Analytics (NDA)10.1145/3327964.3328498(1-10)Online publication date: 30-Jun-2019
https://dl.acm.org/doi/10.1145/3327964.3328498
Show More Cited By

Multilevel algorithms for partitioning power-law graphs
1. Mathematics of computing
  1. Discrete mathematics
    1. Graph theory

Recommendations

Multilevel hypergraph partitioning: applications in VLSI domain

In this paper, we present a new hypergraph-partitioning algorithm that is based on the multilevel paradigm. In the multilevel paradigm, a sequence of successively coarser hypergraphs is constructed. A bisection of the smallest hypergraph is computed and ...
Parallel multilevel k-way partitioning scheme for irregular graphs
Supercomputing '96: Proceedings of the 1996 ACM/IEEE conference on Supercomputing

In this paper we present a parallel formulation of a multilevel k-way graph partitioning algorithm. The multilevel k-way partitioning algorithm reduces the size of the graph by collapsing vertices and edges (coarsening phase), finds a k-way partition of ...
NEPG: Partitioning Large-Scale Power-Law Graphs
Algorithms and Architectures for Parallel Processing
Abstract
We propose Neighbor Expansion on power-law graph(NEPG), a distributed graph partitioning method based on a specific power-law graph that offers both good scalability and high partitioning quality. NEPG is based on a heuristic method, Neighbor ...

Comments

Information & Contributors

Information

Published In

cover image ACM Other conferences

IPDPS'06: Proceedings of the 20th international conference on Parallel and distributed processing

April 2006

399 pages

ISBN:1424400546

Sponsors

IEEE CS TCPP: IEEE Computer Society Technical Committee on Parallel Processing

In-Cooperation

IEEE TCCA: IEEE Computer Society Technical Committee on Computer Architecture
SIGARCH: ACM Special Interest Group on Computer Architecture
IEEE Computer Society Technical Committee on Distributed Processing

Publisher

IEEE Computer Society

United States

Publication History

Published: 25 April 2006

Check for updates

Qualifiers

Article

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

51
Total Citations
View Citations
0
Total Downloads

Downloads (Last 12 months)0
Downloads (Last 6 weeks)0

Reflects downloads up to 12 Jan 2025

Other Metrics

View Author Metrics

Citations

Cited By

Agarwal SDutta SBhattacharya A(2020)ChiSeLProceedings of the VLDB Endowment10.14778/3401960.340196413:10(1654-1668)Online publication date: 1-Jun-2020
https://dl.acm.org/doi/10.14778/3401960.3401964
Lakhotia KKannan RPati SPrasanna V(2020)GPOPACM Transactions on Parallel Computing10.1145/33809427:1(1-24)Online publication date: 9-Mar-2020
https://dl.acm.org/doi/10.1145/3380942
Kolokasis IPratikakis P(2019)Cut to FitProceedings of the 2nd Joint International Workshop on Graph Data Management Experiences & Systems (GRADES) and Network Data Analytics (NDA)10.1145/3327964.3328498(1-10)Online publication date: 30-Jun-2019
https://dl.acm.org/doi/10.1145/3327964.3328498
Pacaci AÖzsu MBoncz PManegold SAilamaki ADeshpande AKraska T(2019)Experimental Analysis of Streaming Algorithms for Graph PartitioningProceedings of the 2019 International Conference on Management of Data10.1145/3299869.3300076(1375-1392)Online publication date: 25-Jun-2019
https://dl.acm.org/doi/10.1145/3299869.3300076
Chen RShi JChen YZang BGuan HChen H(2019)PowerLyraACM Transactions on Parallel Computing10.1145/32989895:3(1-39)Online publication date: 22-Jan-2019
https://dl.acm.org/doi/10.1145/3298989
Wu YCai WLi ZTan WHou X(2019)Efficient Parallel Simulation over Large-scale Social Contact NetworksACM Transactions on Modeling and Computer Simulation10.1145/326574929:2(1-25)Online publication date: 18-Apr-2019
https://dl.acm.org/doi/10.1145/3265749
Gill GDathathri RHoang LPingali K(2018)A study of partitioning policies for graph analytics on large-scale distributed platformsProceedings of the VLDB Endowment10.14778/3297753.329775412:4(321-334)Online publication date: 1-Dec-2018
https://dl.acm.org/doi/10.14778/3297753.3297754
Dathathri RGill GHoang LDang HBrooks ADryden NSnir MPingali K(2018)Gluon: a communication-optimizing substrate for distributed heterogeneous graph analyticsACM SIGPLAN Notices10.1145/3296979.319240453:4(752-768)Online publication date: 11-Jun-2018
https://dl.acm.org/doi/10.1145/3296979.3192404
Moreira OPopp MSchulz CTakadama K(2018)Evolutionary multi-level acyclic graph partitioningProceedings of the Genetic and Evolutionary Computation Conference10.1145/3205455.3205464(332-339)Online publication date: 2-Jul-2018
https://dl.acm.org/doi/10.1145/3205455.3205464
Heidari SSimmhan YCalheiros RBuyya R(2018)Scalable Graph Processing FrameworksACM Computing Surveys10.1145/319952351:3(1-53)Online publication date: 12-Jun-2018
https://dl.acm.org/doi/10.1145/3199523
Show More Cited By

View Options

View options

Media

Figures

Other

Tables

View Table of Contents