Abstract
Fill-reducing sparse matrix orderings have been a topic of active research for many years. Although most such algorithms are developed and analyzed within a graph-theoretical framework, for reasons of performance the corresponding implementations are typically realized with programming languages devoid of language features necessary to explicitly represent graph abstractions. Recently, generic programming has emerged as a programming paradigm capable of providing high levels of performance in the presence of programming abstractions. In this paper we present an implementation of the Minimum Degree ordering algorithm using the newly-developed Generic Graph Component Library. Experimental comparisons show that, despite our heavy use of abstractions, our implementation has performance indistinguishable from that of a widely used Fortran implementation.
This work was supported by NSF grants ASC94-22380 and CCR95-02710.
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References
Yannanakis, M.: Computing the minimum fill-in is NP-complete. SIAM Journal of Algebraic and Discrete Methods (1981)
Zhong, K.: A sparse matrix package using the standard template library. Master’s thesis, University of Notre Dame (1996)
Kumfert, G., Pothen, A.: An object-oriented collection of minimum degree algorithms. Computing in Object-Oriented Parallel Environments, 95–106 (1998)
Austern, M.H.: Generic Programming and the STL. Addison Wesley Longman, Inc., Reading (1998)
Siek, J.G., Lumsdaine, A.: The matrix template library: A generic programming approach to high performance numerical linear algebra. In: Carmel, D., Oldhhoeft, R.R., Tholburn, M. (eds.) Computing in Object-Oriented Parallel Environments, pp. 59–70 (1998)
Lee, L.-Q., Siek, J.G., Lumsdaine, A.: The generic graph component library. In: OOPSLA 1999 (1999) (accepted)
Lee, M., Stepanov, A.: The standard template library. Technical report, HP Laboratories (February 1995)
Cormen, T.H., Leiserson, C.E., Rivest, R.L.: Introduction to Algorithms. The MIT Press, Cambridge (1990)
Gamma, E., Helm, R., Johnson, R., Vlissides, J.: Design Patterns: Elements of Reusable Object-Oriented Software. Addison Wesley Publishing Company, Reading (1994)
Samaragdakis, Y., Batory, D.: Implementing layered designs with mixin layers. In: The Europe Conference on Object-Oriented Programming (1998)
Ng, E.G., Raghavan, P.: Performance of greedy ordering heuristics for sparse Cholesky factorization. SIAM Journal on Matrix Analysis and Applications (to appear)
Parter, S.: The use of planar graph in Gaussian elimination. SIAM Review 3, 364–369 (1961)
George, A., Liu, J.W.H.: The evolution of the minimum degree ordering algorithm. SIAM Review 31(1), 1–19 (1989)
Amestoy, P., Davis, T.A., Duff, I.S.: An approximation minimum degree ordering algorithm. SIAM J. Matrix Analysis and Applications 17(4), 886–905 (1996)
Liu, J.W.H.: Modification of the minimum-degree algorithm by multiple elimination. ACM Transaction on Mathematical Software 11(2), 141–153 (1985)
Grimes, R.G., Lewis, J.G., Duff, I.S.: User’s guide for the harwell-boeing sparse matrix collection. User’s Manual Release 1, Boeing Computer Services, Seattle, WA (October 1992)
University of Florida sparse matrix collection, http://www-pub.cise.ufl.edu/~davis/sparse/
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© 1999 Springer-Verlag Berlin Heidelberg
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Lee, LQ., Siek, J.G., Lumsdaine, A. (1999). Generic Graph Algorithms for Sparse Matrix Ordering. In: Matsuoka, S., Tholburn, M. (eds) Computing in Object-Oriented Parallel Environments. ISCOPE 1999. Lecture Notes in Computer Science, vol 1732. Springer, Berlin, Heidelberg. https://doi.org/10.1007/10704054_13
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DOI: https://doi.org/10.1007/10704054_13
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