Some Combinatorial Properties of Certain Trees With Applications to Searching and Sorting
Journal of the ACM (JACM)
Samplesort: A Sampling Approach to Minimal Storage Tree Sorting
Journal of the ACM (JACM)
Increasing the efficiency of quicksort
Communications of the ACM
Algorithm 347: an efficient algorithm for sorting with minimal storage [M1]
Communications of the ACM
An empirical study of minimal storage sorting
Communications of the ACM
Hi-index | 48.22 |
An integral equation is derived for the generating function for binary tree values, the values reflecting sorting effort. The analysis does not assume uniformly distributed branching ratios, and therefore is applicable to a family of sorting algorithms discussed by Hoare, Singleton, and van Emden. The solution to the integral equation indicates that using more advanced algorithms in the family makes only minor reductions in the expected sorting efforts, but substantially reduces the variance in sorting effort.Statistical tests of the values of several thousand trees containing up to 10,000 points have given first, second, and third moments of the value distribution function in satisfactory agreement with the moments computed from the generating function. The empirical tests, as well as the analytical results, are in agreement with previously pubished results for the first moment in the cases of uniform and nonuniform distribution of branching ratio, and for the second moment in the case of uniform distribution of branching ratio.