The methods currently in use and previously proposed for the choice of a root in minimal storage tree sorting are in reality methods for making inefficient statistical estimates of the median of the sequence to be sorted. By making efficient use of the information in a random sample chosen during input of the sequence to be sorted, significant improvements over ordinary minimal storage tree sorting can be made.A procedure is proposed which is a generalization of minimal storage tree sorting and which has the following three properties: (a) There is a significant improvement (over ordinary minimal storage tree sorting) in the expected number of comparisons required to sort the input sequence. (b) The procedure is statistically insensitive to bias in the input sequence. (c) The expected number of comparisons required by the procedure approaches (slowly) the information-theoretic lower bound on the number of comparisons required. The procedure is, therefore, "asymptotically optimal."

Matrix representations and operations are examined for the purpose of minimizing the page faulting occurring in a paged memory system. It is shown that carefully designed matrix algorithms can lead to enormous savings in the number of page faults occurring when only a small part of the total matrix can be in main memory at one time. Examination of addition, multiplication, and inversion algorithms shows that a partitioned matrix representation (i.e. one submatrix or partition per page) in most cases induced fewer page faults than a row-by-row representation. The number of page-pulls required by these matrix manipulation algorithms is also studied as a function of the number of pages of main memory available to the algorithm.

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