Relational division: four algorithms and their performance

Three known algorithms for relational division, the algebra operator used to express universal quantification (for-all conditions) and an algorithm called hash-division are outlined. By comparing the algorithms analytically and experimentally, it is shown that the algorithm provides performance competitive with or superior to that of techniques used to date, namely techniques using sorting or aggregate functions. Furthermore, the algorithm can eliminate duplicates in the divisor on the fly, ignores duplicates in the dividend, and allows two kinds of partitioning, either of which can be used to resolve hash table overflow or to efficiently implement the algorithm on a multiprocessor system.<>