Abstract
A standard representation of a sparse matrix is a structure where non-zero elements are linked in rows and columns. A general graph structure corresponding to this representation is defined. The problem of partitioning such a graph into fixed size blocks, so that the number of inter-block links is minimized, is shown to be NP-complete.
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References
B. W. Kernighan,Optimal sequential partitions of graphs, Journal of ACM 18, 1 (January 1979), 34–40.
M. R. Garey and D. S. Johnson,Computers, Complexity and Intractability: A Guide to the Theory of NP-completeness, H. P. Freeman and Sons, San Francisco California, (1979).
E. Horowitz and S. Sahni,Fundamentals of Data Structures, Computer Science Press, Potomac, Maryland, (1976).
L. Hyafil and R. L. Rivest,Graph partitioning and constructing optimal decision-trees are polynomial complete problems, IRIA report 33 (October 1973).
J. A. Lukes,Efficient algorithm for the partitioning of trees, IBM Journal of Research and Development 18, 3 (May 1974), 217–224.
J. P. Malmquist,Storage Allocation for Access Path Minimization in Network-Structured Data Bases, Ph.D. Thesis, The Pennsylvania State University, University Park, Pennsylvania, (May 1979).
D. E. Knuth,The Art of Computer Programming, Volume 1: Fundamental Algorithms, Addison-Wesley, Reading, Massachusetts (1973).
M. Schkolnick,A clustering algorithm for hierarchical structures, ACM Transactions on Database Systems 2, 1 (March 1977), 27–44.
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Supported by NSF Grant MCS-8004337.
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Malmquist, J.P., Robertson, E.L. On the complexity of partitioning sparse matrix representations. BIT 24, 60–68 (1984). https://doi.org/10.1007/BF01934515
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DOI: https://doi.org/10.1007/BF01934515