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 Troy Lee

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Average citations per article1.60
Citation Count16
Publication count10
Publication years2013-2017
Available for download4
Average downloads per article121.00
Downloads (cumulative)484
Downloads (12 Months)195
Downloads (6 Weeks)20
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10 results found Export Results: bibtexendnoteacmrefcsv

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1 published by ACM
September 2017 Journal of the ACM (JACM): Volume 64 Issue 5, October 2017
Publisher: ACM
Bibliometrics:
Citation Count: 0
Downloads (6 Weeks): 12,   Downloads (12 Months): 102,   Downloads (Overall): 102

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In 1986, Saks and Wigderson conjectured that the largest separation between deterministic and zero-error randomized query complexity for a total Boolean function is given by the function f on n = 2 k bits defined by a complete binary tree of NAND gates of depth k , which achieves R ...
Keywords: query complexity, Decision trees, quantum algorithms

2
July 2017 CCC '17: Proceedings of the 32nd Computational Complexity Conference
Publisher: Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik
Bibliometrics:
Citation Count: 0

One of the best lower bound methods for the quantum communication complexity of a function H (with or without shared entanglement) is the logarithm of the approximate rank of the communication matrix of H. This measure is essentially equivalent to the approximate γ 2 norm and generalized discrepancy, and subsumes ...
Keywords: communication complexity, quantum information, lower bounds, quantum computing, logrank

3
March 2017 Computational Complexity: Volume 26 Issue 1, March 2017
Publisher: Birkhauser Verlag
Bibliometrics:
Citation Count: 0

Common information was introduced by Wyner (IEEE Trans Inf Theory 21(2):163---179, 1975) as a measure of dependence of two random variables. This measure has been recently resurrected as a lower bound on the logarithm of the nonnegative rank of a nonnegative matrix in Braun and Pokutta (Proceedings of FOCS, 2013) ...
Keywords: Common information, Nonnegative rank, 94A17, Information theory

4
February 2017 Algorithmica: Volume 77 Issue 2, February 2017
Publisher: Springer-Verlag New York, Inc.
Bibliometrics:
Citation Count: 0

We show that the quantum query complexity of detecting if an n-vertex graph contains a triangle is $$O(n^{9/7})$$O(n9/7). This improves the previous best algorithm of Belovs (Proceedings of 44th symposium on theory of computing conference, pp 77---84, 2012) making $$O(n^{35/27})$$O(n35/27) queries. For the problem of determining if an operation $$\circ ...
Keywords: Quantum algorithms, Associativity testing, Learning graphs, Query complexity, Triangle testing

5
September 2016 Journal of Computer and System Sciences: Volume 82 Issue 6, September 2016
Publisher: Academic Press, Inc.
Bibliometrics:
Citation Count: 0

Information-theoretic methods are a powerful tool in communication complexity, providing, in particular, elegant and tight lower bounds on disjointness in the number-in-the-hand (NIH) model. In this paper, we study the applicability of information theoretic methods to the multi-party number-on-the-forehead model (NOF). The lower bound on disjointness in the NIH model ...
Keywords: Communication complexity, Number-on-the-forehead, Informational complexity, Hellinger volume

6 published by ACM
June 2016 STOC '16: Proceedings of the forty-eighth annual ACM symposium on Theory of Computing
Publisher: ACM
Bibliometrics:
Citation Count: 2
Downloads (6 Weeks): 3,   Downloads (12 Months): 48,   Downloads (Overall): 115

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In 1986, Saks and Wigderson conjectured that the largest separation between deterministic and zero-error randomized query complexity for a total boolean function is given by the function f on n =2 k bits defined by a complete binary tree of NAND gates of depth k , which achieves R 0 ...
Keywords: Monte Carlo, Randomized algorithms, Deterministic algorithms, Las Vegas, Quantum algorithms

7
May 2016 CCC '16: Proceedings of the 31st Conference on Computational Complexity
Publisher: Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik
Bibliometrics:
Citation Count: 0

We study how well functions over the boolean hypercube of the form f k ( x ) = (| x | - k )(| x | - k - 1) can be approximated by sums of squares of low-degree polynomials, obtaining good bounds for the case of approximation in ℓ ...
Keywords: extension complexity, quantum query complexity in expectation, approximation theory, positivstellensatz refutations of knapsack, sum-of-squares degree

8
December 2013 NIPS'13: Proceedings of the 26th International Conference on Neural Information Processing Systems - Volume 2
Publisher: Curran Associates Inc.
Bibliometrics:
Citation Count: 2

In the matrix completion problem the aim is to recover an unknown real matrix from a subset of its entries. This problem comes up in many application areas, and has received a great deal of attention in the context of the netflix prize. A central approach to this problem is ...

9 published by ACM
June 2013 STOC '13: Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Publisher: ACM
Bibliometrics:
Citation Count: 7
Downloads (6 Weeks): 3,   Downloads (12 Months): 32,   Downloads (Overall): 221

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We study the ε-rank of a real matrix A, defined for any ε > 0 as the minimum rank over matrices that approximate every entry of A to within an additive ε. This parameter is connected to other notions of approximate rank and is motivated by problems from various topics ...
Keywords: approximate rank, nash equilibria, convex body, covering number

10
January 2013 SODA '13: Proceedings of the twenty-fourth annual ACM-SIAM symposium on Discrete algorithms
Publisher: Society for Industrial and Applied Mathematics
Bibliometrics:
Citation Count: 5
Downloads (6 Weeks): 2,   Downloads (12 Months): 13,   Downloads (Overall): 46

Full text available: PDFPDF
We show that the quantum query complexity of detecting if an n -vertex graph contains a triangle is O ( n 9/7 ). This improves the previous best algorithm of Belovs [2] making O ( n 35/27 ) queries. For the problem of determining if an operation o : S ...



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