期刊
RANDOM STRUCTURES & ALGORITHMS
卷 48, 期 3, 页码 612-638出版社
WILEY
DOI: 10.1002/rsa.20598
关键词
randomized decision tree; recursive majority
资金
- French ANR Blanc Project [ANR-12-BS02-005]
- European Commission IST STREP projects Quantum Computer Science (QCS) [25591]
- Quantum Algorithms (QALGO) [60070]
- NSERC Canada
- Government of Canada Through Industry Canada
- Province of Ontario through MRI
- Singapore Ministry of Education and National Research Foundation
- Tier 3 Grant Random Numbers from Quantum Process
- MTA RAMKI Lendulet Cryptography Research Group, NSERC
- Hungarian OTKA Grant [NN-102029]
- Zheijang Normal University
We consider the randomized decision tree complexity of the recursive 3-majority function. We prove a lower bound of (1/2-delta) . 2.57143(h) for the two-sided-error randomized decision tree complexity of evaluating height h formulae with error delta is an element of [0, 1/2). This improves the lower bound of (1-2 delta)(7/3) h given by Jayram, Kumar, and Sivakumar (STOC'03), and the one of (1-2 delta) . 2.55(h) given by Leonardos (ICALP'13). Second, we improve the upper bound by giving a new zero-error randomized decision tree algorithm that has complexity at most (1.007) . 2.64944(h). The previous best known algorithm achieved complexity (1.004) . 2.65622(h). The new lower bound follows from a better analysis of the base case of the recursion of Jayram et al. The new algorithm uses a novel interleaving of two recursive algorithms. (C) 2015 Wiley Periodicals, Inc.
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