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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
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.
Author information
Authors and Affiliations
Additional information
Supported by NSF Grant MCS-8004337.
Rights and permissions
About this article
Cite this article
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
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01934515