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Abstract: Let X = (x 0 ; : : : ; xn\Gamma1 ) be a sequence of n numbers. For ffl ? 0, we say that x i is an ffl-approximate median if the number of elements strictly less than x i and the number of elements strictly greater than x i are each less than (1 + ffl) n 2 . We consider the quantum query complexity of computing an ffl-approximate median, given the sequence X as an oracle. We prove a lower bound of\Omega\Gamma/42 f 1 ffl ; ng) queries for any quantum algorithm that computes an... (Update)
Context of citations to this paper: More
...mean on any input x. Charikar et al. CCMN00] prove a lower bound for ratio approximation of the frequency moment of order 0. Nayak and Wu [NW99] give a lower bound on the quantum query complexity of the median and some other statistics. Sampling algorithms can be viewed as a...
...mean on any input x. Charikar et al. 9] prove a lower bound for ratio approximation of the frequency moment of order 0. Nayak and Wu [22] give a lower bound on the quantum query complexity of the median and some other statistics. Statistical decision theory [4] studies the...
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BibTeX entry: (Update)
A. Nayak and F. Wu. The quantum query complexity of approximating the median and related statistics. In Proceedings of 31th STOC, 1999. To appear. quant-ph/9804066. http://citeseer.ist.psu.edu/nayak99quantum.html More
@inproceedings{ nayak99quantum,
author = "Ashwin Nayak and Felix Wu",
title = "The quantum query complexity of approximating the median and related statistics",
pages = "384--393",
year = "1999",
url = "citeseer.ist.psu.edu/nayak99quantum.html" }
Citations (may not include all citations):210 A fast quantum mechanical algorithm for database search - Grover - 1996
174 Time bounds for selection (context) - Blum, Floyd et al. - 1973 DBLP
102 Strengths and weaknesses of quantum computing - Bennett, Bernstein et al. - 1997 ACM DBLP
73 Tight bounds on quantum searching - Boyer, Brassard et al. - 1998 ACM
53 The Chebyshev polynomials (context) - Rivlin - 1974
49 Quantum lower bounds by polynomials - Beals, Buhrman et al. - 1998 ACM DBLP
30 Quantum counting - Brassard, Hyer et al. - 1998 ACM DBLP
22 A framework for fast quantum mechanical algorithms (context) - Grover - 1998 ACM DBLP
20 Rational approximation of real functions (context) - Petrushev, Popov - 1987
18 the degree of polynomials that approximate symmetric boolean.. (context) - Paturi - 1992
12 A quantum algorithm for finding the minimum - Durr, Hyer - 1996
11 Quantum amplitude amplification and estimation - Brassard, Hyer et al. - 1998
10 counting and amplitude amplification by eigenvector analysis (context) - Mosca - 1998
7 A fast quantum mechanical algorithm for estimating the media.. (context) - Grover - 1996
6 classical communication and computation (context) - Buhrman, Cleve et al. - 1998
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