Two selection algorithms

Abstract

The problem to find the kth smallest of n elements has been considered as a significant problem in the combinatorial area. In this thesis, two efficient selection algorithms, pSELECT and HSELECT, are presented. The former has a practical upper bound of average case complexity on the number of pairwise comparisons. The later solves the selection problem through efficient use of a hardware sorter. Based on multiselection, a new join method is proposed where the join operation of the relational database management system is a costly operation and the most important operation due to its frequent uses. The algorithm pSELECT mainly consists of a determination step of a partitioning element and a partition step to divide elements into two parts. The partitioning element is estimated from the cumulative frequency distribution of a small sample by using the theory of nonparametric statistics. The expected number of comparisons is n + min(k, n-k) + O($n^{2/3}$) where the sample size is approximately $n^{2/3}$. The experimental results show that the performance of the algorithm is improved, compared to the two known selection algorithms, particularly when the selection index is near to the median. The algorithm HSELECT uses the property of quantiles of each sorted columns which are generated by a special purpose sorter. When a pipeline merge sorter is used, the comparison complexity of the algorithm is 1. 4167n+o(n) in the worst case, provided that the capacity of the sorter is 256 elements. The comparison complexity of the algorithm decreases as the capacity of the sorter increases. Since relation sizes are usually too large to fit in main memory, the join operation may require more than one scan of all tuples of both relations. A new join algorithm which employs a selection algorithm as a basic part of divide-and-conquer strategy is presented to reduce the number of input/output accesses. The performance of the new algorithm is analyzed on the number of input/o...