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<p>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.</p>
upper bounds; sorting; joining; relations; duplicate values; attribute columns; computational complexity; distinct tuple values; multirelation; cardinality; distinct elements; worst time complexity; binary comparisons; lower bounds; three-branch comparisons; natural join operation; computational complexity; database theory; relational databases; sorting

A. Sood and M. Abdelguerfi, "Computational Complexity of Sorting and Joining Relations with Duplicates," in IEEE Transactions on Knowledge & Data Engineering, vol. 3, no. , pp. 496-503, 1991.
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