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Search using queries on indistinguishable items

Author(s): Braverman, Mark; Oshri, G

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Abstract: We investigate the problem of determining a set S of k indistinguishable integers in the range [1, n]. The algorithm is allowed to query an integer q 2 [1, n], and receive a response comparing this integer to an integer randomly chosen from S. The algorithm has no control over which element of S the query q is compared to. We show tight bounds for this problem. In particular, we show that in the natural regime where k ≤ n, the optimal number of queries to attain n- (1) error probability is Θ (k3 log n). In the regime where k ≤ n, the optimal number of queries is Θ (n2k log n). Our main technical tools include the use of information theory to derive the lower bounds, and the application of noisy binary search in the spirit of Feige, Raghavan, Peleg, and Upfal (1994). In particular, our lower bound technique is likely to be applicable in other situations that involve search under uncertainty.
Publication Date: 2013
Electronic Publication Date: 2013
Citation: Braverman, M, Oshri, G. (2013). Search using queries on indistinguishable items. 20 (610 - 621. doi:10.4230/LIPIcs.STACS.2013.610
DOI: doi:10.4230/LIPIcs.STACS.2013.610
Pages: 610 - 621
Type of Material: Conference Article
Journal/Proceeding Title: 30th International Symposium on Theoretical Aspects of Computer Science
Version: Author's manuscript

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