메뉴 건너뛰기




Volumn 32, Issue 4, 2010, Pages 2418-2446

Distributed-memory parallel algorithms for distance-2 coloring and related problems in derivative computation

Author keywords

Automatic differentiation; Combinatorial scientific computing; Distance 2 graph coloring; Distributed memory parallel algorithms; Hessian computation; Jacobian computation; Sparsity exploitation

Indexed keywords

CLUSTERING ALGORITHMS; COLORING; COMPUTATIONAL COMPLEXITY; COMPUTATIONAL EFFICIENCY; GRAPH THEORY; HEURISTIC ALGORITHMS; ITERATIVE METHODS; MEMORY ARCHITECTURE; OPTIMIZATION;

EID: 77955693754     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/080732158     Document Type: Article
Times cited : (26)

References (31)
  • 1
    • 0142075417 scopus 로고    scopus 로고
    • On powers of chordal graphs and their colorings
    • G. AGNARSSON, R. GREENLAW, AND M. M. HALLDóRSSON, On powers of chordal graphs and their colorings, Congr. Numer., 100 (2000), pp. 41-65.
    • (2000) Congr. Numer. , vol.100 , pp. 41-65
    • Agnarsson, G.1    Greenlaw, R.2    Halldórsson, M.M.3
  • 3
    • 0036060795 scopus 로고    scopus 로고
    • A fully asynchronous multifrontal solver using distributed dynamic scheduling
    • P. R. AMESTOY, I. S. DUFF, J.-Y. L'EXCELLENT, AND J. KOSTER, A fully asynchronous multifrontal solver using distributed dynamic scheduling, SIAM J. Matrix Anal. Appl., 23 (2001), pp. 15-41.
    • (2001) SIAM J. Matrix Anal. Appl. , vol.23 , pp. 15-41
    • Amestoy, P.R.1    Duff, I.S.2    L'Excellent, J.-Y.3    Koster, J.4
  • 7
    • 0033360524 scopus 로고    scopus 로고
    • Hypergraph-partitioning-based decomposition for parallel sparse-matrix vector multiplication
    • U. V. CATALYUREK AND C. AYKANAT, Hypergraph-partitioning-based decomposition for parallel sparse-matrix vector multiplication, IEEE Trans. Parallel Distrib. System, 10 (1999), pp. 673-693.
    • (1999) IEEE Trans. Parallel Distrib. System , vol.10 , pp. 673-693
    • Catalyurek, U.V.1    Aykanat, C.2
  • 8
    • 0000421410 scopus 로고
    • Estimation of sparse Jacobian matrices and graph coloring problems
    • T. F. COLEMAN AND J. J. MORé, Estimation of sparse Jacobian matrices and graph coloring problems, SIAM J. Numer. Anal., 20 (1983), pp. 187-209.
    • (1983) SIAM J. Numer. Anal. , vol.20 , pp. 187-209
    • Coleman, T.F.1    Moré, J.J.2
  • 9
    • 0021408208 scopus 로고
    • Estimation of sparse Hessian matrices and graph coloring problems
    • T. F. COLEMAN AND J. J. MORé, Estimation of sparse Hessian matrices and graph coloring problems, Math. Program., 28 (1984), pp. 243-270.
    • (1984) Math. Program. , vol.28 , pp. 243-270
    • Coleman, T.F.1    Moré, J.J.2
  • 10
    • 84952419741 scopus 로고
    • On the estimation of sparse Jacobian matrices
    • A. R. CURTIS, M. J. D. POWELL, AND J. K. REID, On the estimation of sparse Jacobian matrices, J. Inst. Math. Appl., 13 (1974), pp. 117-119.
    • (1974) J. Inst. Math. Appl. , vol.13 , pp. 117-119
    • Curtis, A.R.1    Powell, M.J.D.2    Reid, J.K.3
  • 13
    • 67649958530 scopus 로고    scopus 로고
    • Efficient computation of sparse Hessians using coloring and automatic differentiation
    • A. H. GEBREMEDHIN, A. POTHEN, A. TARAFDAR, AND A. WALTHER, Efficient computation of sparse Hessians using coloring and automatic differentiation, INFORMS J. Comput., 21 (2009), pp. 209-223.
    • (2009) INFORMS J. Comput. , vol.21 , pp. 209-223
    • Gebremedhin, A.H.1    Pothen, A.2    Tarafdar, A.3    Walther, A.4
  • 16
    • 28244465516 scopus 로고    scopus 로고
    • What color is your Jacobian? Graph coloring for computing derivatives
    • A. H. GEBREMEDHIN, F. MANNE, AND A. POTHEN, What color is your Jacobian? Graph coloring for computing derivatives, SIAM Rev., 47 (2005), pp. 629-705.
    • (2005) SIAM Rev. , vol.47 , pp. 629-705
    • Gebremedhin, A.H.1    Manne, F.2    Pothen, A.3
  • 17
    • 36048955533 scopus 로고    scopus 로고
    • New acyclic and star coloring algorithms with application to computing Hessians
    • A. H. GEBREMEDHIN, A. TARAFDAR, F. MANNE, AND A. POTHEN, New acyclic and star coloring algorithms with application to computing Hessians, SIAM J. Sci. Comput., 29 (2007), pp. 1042-1072.
    • (2007) SIAM J. Sci. Comput. , vol.29 , pp. 1042-1072
    • Gebremedhin, A.H.1    Tarafdar, A.2    Manne, F.3    Pothen, A.4
  • 18
    • 0035678671 scopus 로고    scopus 로고
    • A scalable parallel algorithm for incomplete factor preconditioning
    • D. HYSOM AND A. POTHEN, A scalable parallel algorithm for incomplete factor preconditioning, SIAM J. Sci. Comput., 22 (2001), pp. 2194-2215.
    • (2001) SIAM J. Sci. Comput. , vol.22 , pp. 2194-2215
    • Hysom, D.1    Pothen, A.2
  • 19
    • 0028434026 scopus 로고
    • Scalable iterative solution of sparse linear systems
    • M. T. JONES AND P. E. PLASSMANN, Scalable iterative solution of sparse linear systems, Parallel Comput., 20 (1994), pp. 753-773.
    • (1994) Parallel Comput. , vol.20 , pp. 753-773
    • Jones, M.T.1    Plassmann, P.E.2
  • 20
    • 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
  • 21
    • 0035506896 scopus 로고    scopus 로고
    • Models and approximation algorithms for channel assignment in radio networks
    • S. O. KRUMKE, M. V. MARATHE, AND S. S. RAVI, Models and approximation algorithms for channel assignment in radio networks, Wireless Networks, 7 (2001), pp. 575-584.
    • (2001) Wireless Networks , vol.7 , pp. 575-584
    • Krumke, S.O.1    Marathe, M.V.2    Ravi, S.S.3
  • 23
    • 0020765471 scopus 로고
    • Optimal approximation of sparse Hessians and its equivalence to a graph coloring problem
    • S. T. MCCORMICK, Optimal approximation of sparse Hessians and its equivalence to a graph coloring problem, Math. Program., 26 (1983), pp. 153-171.
    • (1983) Math. Program. , vol.26 , pp. 153-171
    • Mccormick, S.T.1
  • 24
    • 52449144607 scopus 로고
    • Heuristics for rapidly four-coloring large planar graphs
    • C. A. MORGENSTERN AND H. D. SHAPIRO, Heuristics for rapidly four-coloring large planar graphs, Algorithmica, 6 (1991), pp. 869-891.
    • (1991) Algorithmica , vol.6 , pp. 869-891
    • Morgenstern, C.A.1    Shapiro, H.D.2
  • 25
    • 0038718854 scopus 로고    scopus 로고
    • The structure and function of complex networks
    • M. E. J. NEWMAN, The structure and function of complex networks, SIAM Rev., 45 (2003), pp. 167-256.
    • (2003) SIAM Rev. , vol.45 , pp. 167-256
    • Newman, M.E.J.1
  • 26
    • 0000495643 scopus 로고
    • On the estimation of sparse Hessian matrices
    • M. J. D. POWELL AND PH. L. TOINT, On the estimation of sparse Hessian matrices, SIAM J. Numer. Anal., 16 (1979), pp. 1060-1074.
    • (1979) SIAM J. Numer. Anal. , vol.16 , pp. 1060-1074
    • Powell, M.J.D.1    Ph. Toint, L.2
  • 27
    • 0001085784 scopus 로고    scopus 로고
    • ILUM: A multi-elimination ILU preconditioner for general sparse matrices
    • Y. SAAD, ILUM: A multi-elimination ILU preconditioner for general sparse matrices, SIAM J. Sci. Comput., 17 (1996), pp. 830-847.
    • (1996) SIAM J. Sci. Comput. , vol.17 , pp. 830-847
    • Saad, Y.1
  • 30
    • 77955680734 scopus 로고    scopus 로고
    • GEORGIA TECH COLLEGE OF COMPUTING, available at
    • GEORGIA TECH COLLEGE OF COMPUTING, GTgraph: A suite of synthetic graph generators, available at http://www-static.cc.gatech.edu/-kamesh/GTgraph/.
    • GTgraph: A Suite of Synthetic Graph Generators


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.