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Selection problems viaM-ary queries

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Abstract

It is well known that, for fixedk, to find thek-th largest ofn elementsn+(k−1)log2 n+Θ(1) comparisons are necessary and sufficient. But do the same bounds apply if we use a different type of query? We show that the arity of the queries is relevant. In particular, we present upper and lower bounds for finding the maximum using 3-ary or 4-ary Boolean (YES/NO answers) queries. We also study general (e.g.,max, sort) 3-ary queries, and show bounds for finding the maximum and the second largest. For sort queries we show matching upper and lower bounds.

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Guimarães, K.S., Gasarch, W.I. & Purtilo, J. Selection problems viaM-ary queries. Comput Complexity 2, 256–276 (1992). https://doi.org/10.1007/BF01272077

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