메뉴 건너뛰기




Volumn 32, Issue 2, 2010, Pages 656-683

ON two-dimensional sparse matrix partitioning: Models, methods, and a recipe

Author keywords

Combinatorial scientific computing; Hypergraph partitioning; Parallel matrix vector multiplication; Sparse matrix partitioning; Two dimensional partitioning

Indexed keywords

GRAPH THEORY;

EID: 77950793269     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/080737770     Document Type: Article
Times cited : (95)

References (51)
  • 1
    • 41449100090 scopus 로고    scopus 로고
    • Multi-level direct K-way hypergraph partitioning with multiple constraints and fixed vertices
    • DOI 10.1016/j.jpdc.2007.09.006, PII S0743731507001724
    • C. AYKANAT, B. B. CAMBAZOGLU, AND B. UÇAR, Multi-level direct k-way hypergraph partitioning with multiple constraints and fixed vertices, J. Parallel Distrib. Comput., 68 (2008), pp. 609-625. (Pubitemid 351458634)
    • (2008) Journal of Parallel and Distributed Computing , vol.68 , Issue.5 , pp. 609-625
    • Aykanat, C.1    Cambazoglu, B.B.2    Ucar, B.3
  • 2
    • 0035480276 scopus 로고    scopus 로고
    • Distributed processing of very large datasets with DataCutter
    • DOI 10.1016/S0167-8191(01)00099-0, PII S0167819101000990
    • M. D. BEYNON, T. KURC, U. CATALYUREK, C. CHANG, A. SUSSMAN, AND J. SALTZ, Distributed processing of very large datasets with DataCutter, Parallel Comput., 27 (2001), pp. 1457- 1478. (Pubitemid 32723674)
    • (2001) Parallel Computing , vol.27 , Issue.11 , pp. 1457-1478
    • Beynon, M.D.1    Kurc, T.2    Catalyurek, U.3    Chang, C.4    Sussman, A.5    Saltz, J.6
  • 3
    • 31444439570 scopus 로고    scopus 로고
    • Communication balancing in parallel sparse matrix-vector multiplication
    • R. H. BISSELING AND W. MEESEN, Communication balancing in parallel sparse matrix-vector multiplication, Electron. Trans. Numer. Anal., 21 (2005), pp. 47 - 65. (Pubitemid 43152783)
    • (2005) Electronic Transactions on Numerical Analysis , vol.21 , pp. 47-65
    • Bisseling, R.H.1    Meesen, W.2
  • 4
    • 38249010798 scopus 로고
    • A new mapping heuristic based on mean field annealing
    • T. BULTAN AND C. AYKANAT, A new mapping heuristic based on mean field annealing,J. Parallel Distrib. Comput., 16 (1992), pp. 292-305.
    • (1992) J. Parallel Distrib. Comput. , vol.16 , pp. 292-305
    • Bultan, T.1    Aykanat, C.2
  • 5
    • 0028405844 scopus 로고
    • Massively parallel methods for engineering and science problems
    • W. CAMP, S. J. PLIMPTON, B. HENDRICKSON, AND R. W. LELAND, Massively parallel methods for engineering and science problems, Commun. ACM, 37 (1994), pp. 31-41.
    • (1994) Commun. ACM , vol.37 , pp. 31-41
    • Camp, W.1    Plimpton, S.J.2    Hendrickson, B.3    Leland, R.W.4
  • 7
    • 10344247945 scopus 로고    scopus 로고
    • Hypergraph models for sparse matrix partitioning and reordering
    • Bilkent University, Computer Engineering and Information Science, Ankara, Turkey
    • U. V. CATALYUREK, Hypergraph Models for Sparse Matrix Partitioning and Reordering,Ph.D. thesis, Bilkent University, Computer Engineering and Information Science, Ankara, Turkey, 1999,http://www.cs.bilkent.edu.tr/tech- reports/1999/ABSTRACTS.1999.html.
    • (1999) Ph.D. Thesis
    • Catalyurek, U.V.1
  • 8
    • 84947911090 scopus 로고    scopus 로고
    • Decomposing Irregularly Sparse Matrices for Parallel Matrix-Vector Multiplication
    • Parallel Algorithms for Irregularly Structured Problems
    • U. V. CATALYUREK AND C. AYKANAT, Decomposing irregularly sparse matrices for parallel matrix-vector multiplications, in Proceedings of the 3rd International Symposium on Solving Irregularly Structured Problems in Parallel, Irregular'96, Lecture Notes in Comput. Sci. 1117, Springer-Verlag, New York, 1996, pp. 75-86. (Pubitemid 126107937)
    • (1996) LECTURE NOTES IN COMPUTER SCIENCE , Issue.1117 , pp. 75-86
    • Catalyuerek, U.V.1    Aykanat, C.2
  • 9
    • 0033360524 scopus 로고    scopus 로고
    • Hypergraph-partitioning-based decomposition for parallel sparse-matrix vector multiplication
    • DOI 10.1109/71.780863
    • U. V. CATALYUREK AND C. AYKANAT, Hypergraph-partitioning based decomposition for parallel sparse-matrix vector multiplication, IEEE Trans. Parallel Distrib. Syst., 10 (1999), pp. 673-693. (Pubitemid 30500688)
    • (1999) IEEE Transactions on Parallel and Distributed Systems , vol.10 , Issue.7 , pp. 673-693
    • Catalyurek, U.V.1    Aykanat, C.2
  • 10
  • 12
    • 41449105445 scopus 로고    scopus 로고
    • A hypergraph-partitioning approach for coarse-grain decomposition
    • Denver, CO
    • U. V. ÇATALYÜREK AND C. AYKANAT, A hypergraph-partitioning approach for coarse-grain decomposition, in ACM/IEEE SC2001, Denver, CO, 2001.
    • (2001) ACM/IEEE SC2001
    • Çatalyürek, U.V.1    Aykanat, C.2
  • 15
    • 0012453312 scopus 로고    scopus 로고
    • The University of Florida sparse matrix collection
    • CISE Department, University of Florida, Gainesville, FL
    • T. DAVIS, The University of Florida Sparse Matrix Collection, Technical report REP-2007-298, CISE Department, University of Florida, Gainesville, FL, 2007.
    • (2007) Technical Report REP-2007-298
    • Davis, T.1
  • 16
    • 37549003336 scopus 로고    scopus 로고
    • Mapreduce: Simplified data processing on large clusters
    • J. DEAN AND S. GHEMAWAT, Mapreduce: Simplified data processing on large clusters, Commun. ACM, 51 (2008), pp. 107-113.
    • (2008) Commun. ACM , vol.51 , pp. 107-113
    • Dean, J.1    Ghemawat, S.2
  • 17
    • 28244496090 scopus 로고    scopus 로고
    • Benchmarking optimization software with performance profiles
    • E. D. DOLAN AND J. J. MORE, Benchmarking optimization software with performance profiles,Math. Program., 91 (2002), pp. 201-213.
    • (2002) Math. Program. , vol.91 , pp. 201-213
    • Dolan, E.D.1    More, J.J.2
  • 18
    • 0033340171 scopus 로고    scopus 로고
    • Object-relational queries into multidimensional databases with the active data repository
    • R. FERREIRA, T. KURC, M. BEYNON, C. CHANG, A. SUSSMAN, AND J. SALTZ, Object-relational queries into multi-dimensional databases with the active data repository, Parallel Process. Lett., 9 (1999), pp. 173-195. (Pubitemid 30511227)
    • (1999) Parallel Processing Letters , vol.9 , Issue.2 , pp. 173-195
    • Ferreira, R.1
  • 19
    • 84883471289 scopus 로고    scopus 로고
    • Graph Partitioning and Parallel Solvers: Has the Emperor No Clothes?
    • Solving Irregularly Structured Problems in Parallel
    • B. HENDRICKSON, Graph Partitioning and Parallel Solvers: Has the Emperor No Clothes?, Lecture Notes in Comput. Sci. 1457, Springer-Verlag, New York, 1998, pp. 218-225. (Pubitemid 128115488)
    • (1998) LECTURE NOTES IN COMPUTER SCIENCE , Issue.1457 , pp. 218-225
    • Hendrickson, B.1
  • 20
    • 0001108827 scopus 로고    scopus 로고
    • Graph partitioning models for parallel computing
    • B. HENDRICKSON AND T. G. KOLDA, Graph partitioning models for parallel computing, Parallel Comput., 26 (2000), pp. 1519-1534.
    • (2000) Parallel Comput. , vol.26 , pp. 1519-1534
    • Hendrickson, B.1    Kolda, T.G.2
  • 21
    • 0034497251 scopus 로고    scopus 로고
    • Partitioning rectangular and structurally unsymmetric sparse matrices for parallel processing
    • DOI 10.1137/S1064827598341475
    • 21] B. HENDRICKSON AND T. G. KOLDA, Partitioning rectangular and structurally unsymmetric sparse matrices for parallel processing, SIAM J. Sci. Comput., 21 (2000), pp. 2048-2072. (Pubitemid 32076056)
    • (2000) SIAM Journal of Scientific Computing , vol.21 , Issue.6 , pp. 2048-2072
    • Hendrickson, B.1    Kolda, T.G.2
  • 25
    • 0029375750 scopus 로고
    • Partitioning unstructured computational graphs for nonuniform and adaptive environments
    • M. KADDOURA, C. W. OU, AND S. RANKA, Partitioning unstructured computational graphs for nonuniform and adaptive environments, IEEE Parallel Distrib. Technol., 3 (1995), pp. 63-69.
    • (1995) IEEE Parallel Distrib. Technol. , vol.3 , pp. 63-69
    • Kaddoura, M.1    Ou, C.W.2    Ranka, S.3
  • 26
    • 0032131147 scopus 로고    scopus 로고
    • A fast and high quality multilevel scheme for partitioning irregular graphs
    • PII S1064827595287997
    • G. KARYPIS AND V. KUMAR, A fast and high quality multilevel scheme for partitioning irregular graphs, SIAM J. Sci. Comput., 20 (1998), pp. 359-392. (Pubitemid 128689516)
    • (1998) SIAM Journal of Scientific Computing , vol.20 , Issue.1 , pp. 359-392
    • Karypis, G.1    Kumar, V.2
  • 27
    • 0004030623 scopus 로고    scopus 로고
    • Technical report 98-019, University of Minnesota, Department of Computer Science/Army HPC Research Center, Minneapolis, MN
    • G. KARYPIS AND V. KUMAR, Multilevel Algorithms for Multi-constraint Graph Partitioning, Technical report 98-019, University of Minnesota, Department of Computer Science/Army HPC Research Center, Minneapolis, MN, 1998.
    • (1998) Multilevel Algorithms for Multi-constraint Graph Partitioning
    • Karypis, G.1    Kumar, V.2
  • 31
    • 0033903498 scopus 로고    scopus 로고
    • Image-space decomposition algorithms for sort-first parallel volume rendering of unstructured grids
    • DOI 10.1023/A:1008169609963
    • H. KUTLUCA, T. M. KURC, AND C. AYKANAT, Image-space decomposition algorithms for sort- first parallel volume rendering of unstructured grids, J. Supercomputing, 15 (2001), pp. 51-93. (Pubitemid 30542298)
    • (2000) Journal of Supercomputing , vol.15 , Issue.1 , pp. 51-93
    • Kutluca, H.1    Kurc, T.M.2    Aykanat, C.3
  • 32
    • 0029328131 scopus 로고
    • Mapping molecular dynamics computations on to hypercubes
    • V. LAKAMSANI, L. N. BHUYAN, AND D. S. LINTHICUM, Mapping molecular dynamics computations on to hypercubes, Parallel Comput., 21 (1995), pp. 993-1013
    • (1995) Parallel Comput. , vol.21 , pp. 993-1013
    • Lakamsani, V.1    Bhuyan, L.N.2    Linthicum, D.S.3
  • 35
    • 0027758344 scopus 로고
    • Distributed memory matrix-vector multiplication and conjugate gradient algorithms
    • Portland, OR
    • J. G. LEWIS AND R. A. VAN DE GEIJN, Distributed memory matrix-vector multiplication and conjugate gradient algorithms, in Proceedings of Supercomputing'93, Portland, OR, 1993, pp. 484-492.
    • (1993) Proceedings of Supercomputing , vol.93 , pp. 484-492
    • Lewis, J.G.1    Van De Geijn, R.A.2
  • 36
    • 84947927365 scopus 로고    scopus 로고
    • Partitioning an Array onto a Mesh of Processors
    • Applied Parallel Computing: Industrial Computation and Optimization
    • F. MANNE AND T. S0REVIK, Partitioning an array onto a mesh of processors, in PARA '96: Proceedings of the Third International Workshop on Applied Parallel Computing, Industrial Computation and Optimization, London, UK, 1996, also in Applied Parallel Computing Industrial Computation and Optimization, Lecture Notes in Comput. Sci, 1184, Springer-Verlag, New York, 1996, pp. 467-477. (Pubitemid 127013643)
    • (1996) LECTURE NOTES IN COMPUTER SCIENCE , Issue.1184 , pp. 467-477
    • Manne, F.1    Soerevik, T.2
  • 37
    • 0029324885 scopus 로고
    • Partitioning of unstructured meshes for load balancing
    • O. C. MARTIN AND S. W. OTTO, Partitioning of unstructured meshes for load balancing, Concurrency: Practice and Experience, 7 (1995), pp. 303-314.
    • (1995) Concurrency: Practice and Experience , vol.7 , pp. 303-314
    • Martin, O.C.1    Otto, S.W.2
  • 38
    • 0001191149 scopus 로고
    • Rectilinear partitioning of irregular data parallel computations
    • D. M. NICOL, Rectilinear partitioning of irregular data parallel computations, J. Parallel Distrib. Comput., 23 (1994), pp. 119-134.
    • (1994) J. Parallel Distrib. Comput. , vol.23 , pp. 119-134
    • Nicol, D.M.1
  • 39
    • 0040667844 scopus 로고
    • Sparse matrix computations on parallel processor arrays
    • A. T. OGIELSKI AND W. AlELLO, Sparse matrix computations on parallel processor arrays, SIAM J. Sci. Comput., 14 (1993), pp. 519-530.
    • (1993) SIAM J. Sci. Comput. , vol.14 , pp. 519-530
    • Ogielski, A.T.1    Alello, W.2
  • 40
    • 10844240770 scopus 로고    scopus 로고
    • Fast optimal load balancing algorithms for 1D partitioning
    • DOI 10.1016/j.jpdc.2004.05.003
    • A. PlNAR AND C. AYKANAT, Fast optimal load balancing algorithms for 1D partitioning,J. Parallel Distrib. Comput., 64 (2004), pp. 974-996. (Pubitemid 40000768)
    • (2004) Journal of Parallel and Distributed Computing , vol.64 , Issue.8 , pp. 974-996
    • Pinar, A.1    Aykanat, C.2
  • 41
    • 0029290074 scopus 로고
    • Data distributions for sparse matrix vector multiplication
    • L. F. ROMERO AND E. L. ZAPATA, Data distributions for sparse matrix vector multiplication,Parallel Comput., 21 (1995), pp. 583-605.
    • (1995) Parallel Comput. , vol.21 , pp. 583-605
    • Romero, L.F.1    Zapata, E.L.2
  • 42
    • 0026239655 scopus 로고
    • Performance effects of irregular communication patterns on massively parallel multiprocessors
    • DOI 10.1016/0743-7315(91)90089-R
    • J. H. SALTZ, S. G. PETITION, H. BERRYMAN, AND A. RlFKIN, Performance effects of irregular communication patterns on massively parallel multiprocessors, J. Parallel Distrib. Comput., 13 (1991), pp. 202-212. (Pubitemid 21710567)
    • (1991) Journal of Parallel and Distributed Computing , vol.13 , Issue.2 , pp. 202-212
    • Saltz Joel1    Petiton Serge2    Berryman Harry3    Rifkin Adam4
  • 43
    • 0345507524 scopus 로고    scopus 로고
    • Technical report 99-003, University of Minnesota, Department of Computer Science/Army HPC Research Center, Minneapolis, MN
    • K. SCHLOEGEL, G. KARYPIS, AND V. KUMAR, A New Algorithm for Multi-objective Graph Partitioning, Technical report 99-003, University of Minnesota, Department of Computer Science/Army HPC Research Center, Minneapolis, MN, 1999.
    • (1999) A New Algorithm for Multi-objective Graph Partitioning
    • Schloegel, K.1    Karypis, G.2    Kumar, V.3
  • 44
    • 84937397986 scopus 로고    scopus 로고
    • Parallel multilevel algorithms for multi-constraint graph partitioning
    • Munich, Germany, Lecture Notes in Comput Sci. 1900, Springer-Verlag, New York
    • K. SCHLOEGEL, G. KARYPIS, AND V. KUMAR, Parallel multilevel algorithms for multi-constraint graph partitioning, in Proceedings of the Euro-Par 2000 Parallel Processing, Munich, Germany, Lecture Notes in Comput. Sci. 1900, Springer-Verlag, New York, 2000, pp. 296-300.
    • (2000) Proceedings of the Euro-Par 2000 Parallel Processing , pp. 296-300
    • Schloegel, K.1    Karypis, G.2    Kumar, V.3
  • 45
    • 45449098681 scopus 로고    scopus 로고
    • Heuristics for a matrix symmetrization problem
    • PPAM 2007 Springer-Verlag, New York
    • B. UÇAR, Heuristics for a matrix symmetrization problem, in PPAM 2007, Lecture Notes in Comput. Sci. 4967, Springer-Verlag, New York, 2008, pp. 717-727.
    • (2008) Lecture Notes in Comput Sci. , vol.4967 , pp. 717-727
    • Uçar, B.1
  • 46
    • 0142183956 scopus 로고    scopus 로고
    • Minimizing Communication Cost in Fine-Grain Partitioning of Sparse Matrices
    • Computer and Information Sciences - ISCIS 2003
    • B. UÇAR AND C. AYKANAT, Minimizing communication cost in fine-grain partitioning of sparse matrices, in ISCIS 2003, Lecture Notes in Comput. Sci. 2869, Springer-Verlag, New York, 2003, pp. 926-933. (Pubitemid 37331739)
    • (2003) LECTURE NOTES IN COMPUTER SCIENCE , Issue.2869 , pp. 926-933
    • Ucar, B.1    Aykanat, C.2
  • 47
    • 10344261407 scopus 로고    scopus 로고
    • Encapsulating multiple communication-cost metrics in partitioning sparse rectangular matrices for parallel matrix-vector multiplies
    • B. UÇAR AND C. AYKANAT, A Library for Parallel Sparse Matrix-vector Multiplies, Technical report BU-CE-0506, Department of Computer Engineering, Bilkent University, Ankara, Turkey, 2005.
    • (2004) SIAM J. Sci. Comput. , vol.25 , pp. 1837-1859
    • Uçar, B.1    Aykanat, C.2
  • 48
    • 41449101917 scopus 로고    scopus 로고
    • Partitioning sparse matrices for parallel preconditioned iterative methods
    • B. UÇAR AND C. AYKANAT, Partitioning sparse matrices for parallel preconditioned iterative methods, SIAM J. Sci. Comput., 29 (2007), pp. 1683-1709
    • (2007) SIAM J. Sci. Comput. , vol.29 , pp. 1683-1709
    • Uçar, B.1    Aykanat, C.2
  • 49
    • 37249078616 scopus 로고    scopus 로고
    • Revisiting hypergraph models for sparse matrix partitioning
    • DOI 10.1137/060662459
    • B. UÇAR AND C. AYKANAT, Revisiting hypergraph models for sparse matrix partitioning,SIAM Rev., 49 (2007), pp. 595-603. (Pubitemid 350263544)
    • (2007) SIAM Review , vol.49 , Issue.4 , pp. 595-603
    • Ucar, B.1    Aykanat, C.2
  • 51
    • 17444414573 scopus 로고    scopus 로고
    • A two-dimensional data distribution method for parallel sparse matrix-vector multiplication
    • DOI 10.1137/S0036144502409019
    • B. VASTENHOUW AND R. H. BISSELING, A two-dimensional data distribution method for parallel sparse matrix-vector multiplication, SIAM Rev., 47 (2005), pp. 67-95. (Pubitemid 40535972)
    • (2005) SIAM Review , vol.47 , Issue.1 , pp. 67-95
    • Vastenhouw, B.1    Bisseling, R.H.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.