Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
skip to main content
article

Multi-level direct K-way hypergraph partitioning with multiple constraints and fixed vertices

Published: 01 May 2008 Publication History

Abstract

K-way hypergraph partitioning has an ever-growing use in parallelization of scientific computing applications. We claim that hypergraph partitioning with multiple constraints and fixed vertices should be implemented using direct K-way refinement, instead of the widely adopted recursive bisection paradigm. Our arguments are based on the fact that recursive-bisection-based partitioning algorithms perform considerably worse when used in the multiple constraint and fixed vertex formulations. We discuss possible reasons for this performance degradation. We describe a careful implementation of a multi-level direct K-way hypergraph partitioning algorithm, which performs better than a well-known recursive-bisection-based partitioning algorithm in hypergraph partitioning with multiple constraints and fixed vertices. We also experimentally show that the proposed algorithm is effective in standard hypergraph partitioning.

References

[1]
Alpert, C.J., Caldwell, A.E., Kahng, A.B. and Markov, I.L., Hypergraph partitioning with fixed vertices. IEEE Trans. Comput.-Aided Design. v19 i2. 267-272.
[2]
Alpert, C.J. and Kahng, A.B., Recent directions in netlist partitioning: a survey. VLSI J. v19 i1--2. 1-81.
[3]
Ashcraft, C., Compressed graphs and the minimum degree algorithm. SIAM J. Sci. Comput. v16 i6. 1404-1411.
[4]
Aykanat, C., Pinar, A. and Çatalyürek, Ü.V., Permuting sparse rectangular matrices into block-diagonal form. SIAM J. Sci. Comput. v25 i6. 1860-1879.
[5]
Berge, C., Graphs and Hypergraphs. 1973. North-Holland Publishing Company, Amsterdam.
[6]
Bisseling, R.H., Byrka, J., Cerav-Erbas, S., Gvozdenovic, N., Lorenz, M., Pendavingh, R., Reeves, C., Roger, M. and Verhoeven, A., Partitioning a call graph. In: Second International Workshop on Combinatorial Scientific Computing,
[7]
Bisseling, R.H. and Flesch, I., Mondriaan sparse matrix partitioning for attacking cryptosystems by a parallel block Lanczos algorithm: a case study. Parallel Comput. v32 i7. 551-567.
[8]
Bui, T.N. and Jones, C., A heuristic for reducing fill in sparse matrix factorization. In: Proceedings of the Sixth SIAM Conference on Parallel Processing for Scientific Computing, pp. 445-452.
[9]
Caldwell, A., Kahng, A. and Markov, I., Improved algorithms for hypergraph bipartitioning. In: Proceedings of the IEEE ACM Asia and South Pacific Design Automation Conference, pp. 661-666.
[10]
Cambazoglu, B.B. and Aykanat, C., Hypergraph-partitioning-based remapping models for image-space-parallel direct volume rendering of unstructured grids. IEEE Trans. Parallel Distributed Systems. v18 i1. 3-16.
[11]
Chang, C., Kurc, T.M., Sussman, A., Çatalyürek, Ü.V. and Saltz, J.H., A hypergraph-based workload partitioning strategy for parallel data aggregation. In: SIAM Conference on Parallel Processing for Scientific Computing,
[12]
Chartrand, G. and Oellermann, O.R., Applied and Algorithmic Graph Theory. 1993. McGraw-Hill, New York.
[13]
Clifton, C., Cooley, R. and Rennie, J., TopCat: data mining for topic identification in a text corpus. IEEE Trans. Knowledge Data Eng. v16 i8. 949-964.
[14]
Ü.V. Çatalyürek, ISPD98 benchmark <http://bmi.osu.edu/∼umit/PaToH/ispd98.html>.
[15]
Ü.V. Çatalyürek, C. Aykanat, Decomposing irregularly sparse matrices for parallel matrix--vector multiplication, Lecture Notes in Computer Science, vol. 1117, 1996, pp. 75--86.
[16]
Ü.V. Çatalyürek, C. Aykanat, PaToH: partitioning tool for hypergraphs, Technical Report, Department of Computer Engineering, Bilkent University, 1999.
[17]
Çatalyürek, Ü.V. and Aykanat, C., Hypergraph-partitioning-based decomposition for parallel sparse-matrix vector multiplication. IEEE Trans. Parallel Distributed Systems. v10 i7. 673-693.
[18]
Çatalyürek, Ü.V. and Aykanat, C., A fine-grain hypergraph model for 2D decomposition of sparse matrices. In: Proceedings of the 15th International Parallel and Distributed Processing Symposium, pp. 118
[19]
Çatalyürek, Ü.V. and Aykanat, C., A hypergraph-partitioning approach for coarse-grain decomposition. In: Proceedings of the 2001 ACM/IEEE Conference on Supercomputing, pp. 28
[20]
Dasdan, A. and Aykanat, C., Two novel multiway circuit partitioning algorithms using relaxed locking. IEEE Trans. Comput.-Aided Design Integrated Circuits Systems. v16 i2. 169-178.
[21]
T. Davis, University of Florida Sparse Matrix Collection <http://www.cise.ufl.edu/research/sparse/matrices>, NA Digest 97 (23) (June 7, 1997).
[22]
E. Demir, C. Aykanat, B.B. Cambazoglu, Clustering spatial networks for aggregate query processing: a hypergraph approach, Inform. Systems, in press.
[23]
E. Demir, C. Aykanat, B.B. Cambazoglu, A link-based storage scheme for efficient aggregate query processing on clustered road networks, Technical Report, BU-CE-0707, Department of Computer Engineering, Bilkent University, 2007.
[24]
Devine, K.D., Boman, E.G., Heaphy, R.T., Bisseling, R. and Çatalyürek, Ü.V., Parallel hypergraph partitioning for scientific computing. In: Proceedings of the IEEE International Parallel and Distributed Processing Symposium,
[25]
Devine, K.D., Boman, E.G., Heaphy, R.T., Hendrickson, B. and Vaughan, C., Zoltan data management services for parallel dynamic applications. Comput. Sci. Eng. v4 i2. 90-97.
[26]
Dingle, N.J., Harrison, P.G. and Knottenbelt, W.J., Uniformization and hypergraph partitioning for the distributed computation of response time densities in very large Markov models. J. Parallel Distributed Comput. v64 i8. 908-920.
[27]
I.S. Duff, S. Riyavong, M.B. van Gijzen, Parallel preconditioners based on partitioning sparse matrices, Technical Report, TR/PA/04/114, CERFACS, 2004.
[28]
C.M. Fiduccia, R.M. Mattheyses, A linear-time heuristic for improving network partitions, in: Proceedings of the 19th ACM/IEEE Design Automation Conference, 1982, pp. 175--181.
[29]
Goldberg, M.K. and Burnstein, M., Heuristic improvement technique for bisection of VLSI networks. In: Proceedings of the IEEE International Conference on Computer Design, pp. 122-125.
[30]
B. Hendrickson, R. Leland, The Chaco user's guide: version 2.0, Technical Report, SAND94-2692, Sandia National Laboratories, 1994.
[31]
Hendrickson, B. and Rothberg, E., Improving the run time and quality of nested dissection ordering. SIAM J. Sci. Comput. v20 i2. 468-489.
[32]
Karypis, G., Aggarwal, R., Kumar, V. and Shekhar, S., Multilevel hypergraph partitioning: applications in VLSI domain. IEEE Trans. Very Large Scale Integration Systems. v7 i1. 69-79.
[33]
G. Karypis, V. Kumar, hMETIS: a hypergraph partitioning package, Technical Report, Department of Computer Science, University of Minnesota, 1998.
[34]
G. Karypis, V. Kumar, MeTiS: a software package for partitioning unstructured graphs, partitioning meshes and computing fill-reducing orderings of sparse matrices, Technical Report, Department of Computer Science, University of Minnesota, 1998.
[35]
G. Karypis, V. Kumar, Multilevel algorithms for multi-constraint graph par-titioning, in: Proceedings of the 1998 ACM/IEEE Conference on Supercomputing, 1998, pp. 1--13.
[36]
Karypis, G. and Kumar, V., Multilevel k-way hypergraph partitioning. VLSI Design. v11 i3. 285-300.
[37]
Kaya, K. and Aykanat, C., Iterative-improvement-based heuristics for adaptive scheduling of tasks sharing files on heterogeneous master--slave environments. IEEE Trans. Parallel Distributed Systems. v17 i8. 883-896.
[38]
Kaya, K., Ucar, B. and Aykanat, C., Heuristics for scheduling file-sharing tasks on heterogeneous systems with distributed repositories. J. Parallel Distributed Comput. v67 i3. 271-285.
[39]
Kernighan, B.W. and Lin, S., An efficient heuristic procedure for partitioning graphs. Bell System Technical J. v49. 291-307.
[40]
G. Khanna, N. Vydyanathan, T.M. Kurc, Ü.V. Çatalyürek, P. Wyckoff, J. Saltz, P. Sadayappan, A hypergraph partitioning based approach for scheduling of tasks with batch-shared IO, in: Proceedings of Cluster Computing and Grid, 2005.
[41]
Koyuturk, M. and Aykanat, C., Iterative-improvement-based declustering heuristics for multi-disk databases. Inform. Systems. v30 i1. 47-70.
[42]
Lengauer, T., Combinatorial Algorithms for Integrated Circuit Layout. 1990. Wiley-Teubner, Chichester.
[43]
Liu, D.R. and Wu, M.Y., A hypergraph based approach to declustering problems. Distributed Parallel Databases. v10 i3. 269-288.
[44]
Ozdal, M.M. and Aykanat, C., Hypergraph models and algorithms for data-pattern-based clustering. Data Mining Knowledge Discovery. v9 i1. 29-57.
[45]
Schweikert, D.G. and Kernighan, B.W., A proper model for the partitioning of electrical circuits. In: Proceedings of the 9th Workshop on Design Automation, pp. 57-62.
[46]
Shekhar, S., Lu, C.-T., Chawla, S. and Ravada, S., Efficient join-index-based spatial-join processing: a clustering approach. IEEE Trans. Knowledge Data Eng. v14 i6. 1400-1421.
[47]
Simon, H.D. and Teng, S.-H., How good is recursive bisection?. SIAM J. Sci. Comput. v18 i5. 1436-1445.
[48]
Trifunovic, A. and Knottenbelt, W.J., Parkway2.0: a parallel multilevel hypergraph partitioning tool. In: Proceedings of the International Symposium on Computer and Information Sciences, pp. 789-800.
[49]
Uçar, B. and Aykanat, C., Encapsulating multiple communication-cost metrics in partitioning sparse rectangular matrices for parallel matrix--vector multiplies. SIAM J. Sci. Comput. v25 i6. 1837-1859.
[50]
B. Uçar, C. Aykanat, Revisiting hypergraph models for sparse matrix partitioning, SIAM Rev. 49 (4) (2007) 543--732.
[51]
Uçar, B. and Aykanat, C., Partitioning sparse matrices for parallel preconditioned iterative methods. SIAM J. Sci. Comput. v29 i4. 1683-1709.
[52]
Uçar, B., Aykanat, C., Pınar, M.C. and Malas, T., Parallel image restoration using surrogate constraints methods. J. Parallel Distributed Comput. v67 i2. 186-204.
[53]
Vastenhouw, B. and Bisseling, R.H., A two-dimensional data distribution method for parallel sparse matrix-vector multiplication. SIAM Rev. v47 i1. 67-95.
[54]
Walshaw, C., Cross, M. and McManus, K., Multiphase mesh partitioning. Appl. Math. Modelling. v25. 123-140.

Cited By

View all
  • (2024)Scalable High-Quality Hypergraph PartitioningACM Transactions on Algorithms10.1145/362652720:1(1-54)Online publication date: 22-Jan-2024
  • (2023)More Recent Advances in (Hyper)Graph PartitioningACM Computing Surveys10.1145/357180855:12(1-38)Online publication date: 2-Mar-2023
  • (2023)High-Quality Hypergraph PartitioningACM Journal of Experimental Algorithmics10.1145/352909027(1-39)Online publication date: 10-Feb-2023
  • Show More Cited By

Recommendations

Comments

Information & Contributors

Information

Published In

Publisher

Academic Press, Inc.

United States

Publication History

Published: 01 May 2008

Author Tags

  1. Direct K-way refinement
  2. Fixed vertices
  3. Hypergraph partitioning
  4. Multi-constraint
  5. Multi-level paradigm
  6. Recursive bisection

Qualifiers

  • Article

Contributors

Other Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

  • Downloads (Last 12 months)0
  • Downloads (Last 6 weeks)0
Reflects downloads up to 15 Oct 2024

Other Metrics

Citations

Cited By

View all
  • (2024)Scalable High-Quality Hypergraph PartitioningACM Transactions on Algorithms10.1145/362652720:1(1-54)Online publication date: 22-Jan-2024
  • (2023)More Recent Advances in (Hyper)Graph PartitioningACM Computing Surveys10.1145/357180855:12(1-38)Online publication date: 2-Mar-2023
  • (2023)High-Quality Hypergraph PartitioningACM Journal of Experimental Algorithmics10.1145/352909027(1-39)Online publication date: 10-Feb-2023
  • (2021)Multi-constraint building partitioning formulation for effective contaminant detection and isolation2016 IEEE Congress on Evolutionary Computation (CEC)10.1109/CEC.2016.7744387(4675-4682)Online publication date: 11-Mar-2021
  • (2019)HyperPRAWProceedings of the 48th International Conference on Parallel Processing10.1145/3337821.3337876(1-10)Online publication date: 5-Aug-2019
  • (2019)Network Flow-Based Refinement for Multilevel Hypergraph PartitioningACM Journal of Experimental Algorithmics10.1145/332987224(1-36)Online publication date: 5-Sep-2019
  • (2018)Partitioning and Communication Strategies for Sparse Non-negative Matrix FactorizationProceedings of the 47th International Conference on Parallel Processing10.1145/3225058.3225127(1-10)Online publication date: 13-Aug-2018
  • (2018)Memetic multilevel hypergraph partitioningProceedings of the Genetic and Evolutionary Computation Conference10.1145/3205455.3205475(347-354)Online publication date: 2-Jul-2018
  • (2018)Partitioning Models for Scaling Parallel Sparse Matrix-Matrix MultiplicationACM Transactions on Parallel Computing10.1145/31552924:3(1-34)Online publication date: 3-Jan-2018
  • (2017)Stochastic shadow detection using a hypergraph partitioning approachPattern Recognition10.1016/j.patcog.2016.09.00863:C(30-44)Online publication date: 1-Mar-2017
  • Show More Cited By

View Options

View options

Get Access

Login options

Media

Figures

Other

Tables

Share

Share

Share this Publication link

Share on social media