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How to Store a Triangular Matrix
July 1992 (vol. 41 no. 7)
pp. 896-899

The problem of storing a triangular matrix so that each row and column is stored as a vector, i.e. the locations form an arithmetic progression, is discussed. Storing rows and columns as vectors can speed up access significantly. It is shown that there is no such storage method that does not waste approximately one-half of the computer memory.

[1] P. Budnick and D. J. Kuck, "The organization and use of parallel memories,"IEEE Trans. Comput., vol. C-20, pp. 1566-1569, Dec. 1971.
[2] H. Garcia-Molina, R. Lipton, and J. Valdes, "A massive memory machine,"IEEE Trans. Comput., vol. C-33, pp. 391-399, May 1984.
[3] G. H. Hardy and E. M. Wright,An Introduction to the Theory of Numbers. London, UK Oxford University Press, 1975.
[4] A. B. Jacobson, L. Good, J. Simonetti, and M. Zucker, "Some simple computational methods to improve the folding of large RNA's,"Nucleic Acids Res., vol. 12, no. 1, pp. 45-52, 1984.
[5] M. Kanehisa and C. DeLisi, "The prediction of a protein and nucleic acid structure: Problems and prospects,"Acta Applicande Machematicae, no. 4, pp. 115-137, 1985.
[6] D. E. Knuth,The Art of Computer Programming, Vol. 1. Reading, MA: Addison-Wesley, 1973.
[7] D. H. Lawrie, "The prime memory system for array access,"IEEE Trans. Comput., vol. C-31, pp. 134-141, 1982.
[8] R. Nussinov, G. Pieczenik, J. R. Griggs, and D. J. Kleitman, "Algorithms for looping matching,"SIAM J. Appl. Math., vol. 35, no. 1, pp. 68-82, 1978.
[9] D. Sankoff, J. B. Kruskal, S. Mainville, and R. J. Cedergren, "Fast algorithms to determine RNA secondary structures containing multiple loops," inTime Wraps, String Edits, and Macromolecules: Theory and Practice of Sequence Comparisons, D. Sankoff and J. B. Kruskal Eds. Reading, MA: Addison-Wesley, 1983, pp. 93-120.
[10] M. Zucker and P. Stiegler, "Optimal computer folding of large RNA sequences using thermodynamics and auxiliary information,"Nucleic Acids Res., vol. 9, no. 1, pp. 133-148, 1981.

Index Terms:
triangular matrix; vector; arithmetic progression; data structures; file organisation.
A.S. LaPaugh, R.J. Lipton, J.S. Sandberg, "How to Store a Triangular Matrix," IEEE Transactions on Computers, vol. 41, no. 7, pp. 896-899, July 1992, doi:10.1109/12.256446
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