Computational complexity of sorting and joining relations with duplicates

It is shown that the existence of duplicate values in some attribute columns has a significant impact on the computational complexity of the sorting and joining operations. This is especially true when the number of distinct tuple values is a small fraction of the total number of tuples. The authors characterize a multirelation M (n, L) by its cardinality n and the number of distinct elements L it contains. Under this characterization, the worst time complexity of sorting such a multirelation with binary comparisons as basic operations is investigated. Upper and lower bounds on the number of three-branch comparisons needed to sort such a multirelation are established. Thereafter, the methodology used to study the complexity of sorting is applied to the natural join operation. It is shown that the existence of duplicate values in the join attribute columns can be exploited to reduce the computational complexity of the natural join operation