We show a general relationship between the number of comparisons and the number of I/O-operations needed to solve a given problem. This relationship enables one to show lower bounds on the number of I/O-operations needed to solve a problem whenever a lower bound on the number of comparisons is known. We use the result to show lower bounds on the I/O-complexity on a number of problems where known techniques only give trivial bounds. Among these are the problems of removing duplicates from a multiset, a problem of great importance in e.g. relational data-base systems, and the problem of determining the mode — the most frequently occurring element — of a multiset. We develop algorithms for these problems in order to show that the lower bounds are tight.
CITATION STYLE
Arge, L., Knudsen, M., & Larsen, K. (1993). A general lower bound on the I/O-complexity of comparison-based algorithms. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 709 LNCS, pp. 84–94). Springer Verlag. https://doi.org/10.1007/3-540-57155-8_238
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