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 Aaron Henry Potechin

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Average citations per article2.71
Citation Count19
Publication count7
Publication years2008-2017
Available for download4
Average downloads per article151.50
Downloads (cumulative)606
Downloads (12 Months)126
Downloads (6 Weeks)20
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1 published by ACM
August 2017 Journal of the ACM (JACM): Volume 64 Issue 4, September 2017
Publisher: ACM
Citation Count: 0
Downloads (6 Weeks): 10,   Downloads (12 Months): 64,   Downloads (Overall): 64

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We separate monotone analogues of L and NL by proving that any monotone switching network solving directed connectivity on n vertices must have size at least n Ω(lg n ) .
Keywords: monotone computation, switching networks, L, directed connectivity, NL, circuit lower bounds

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

In this paper, we show that while almost all functions require exponential size branching programs to compute, for all functions f there is a branching program computing a doubly exponential number of copies of f which has linear size per copy of f. This result disproves a conjecture about non-uniform ...
Keywords: amortization, branching programs, space complexity

January 2016 SODA '16: Proceedings of the twenty-seventh annual ACM-SIAM symposium on Discrete algorithms
Publisher: Society for Industrial and Applied Mathematics
Citation Count: 2
Downloads (6 Weeks): 3,   Downloads (12 Months): 17,   Downloads (Overall): 39

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The problem of finding large cliques in random graphs and its "planted" variant, where one wants to recover a clique of size ω ≫ log ( n ) added to an Erdó's-Rényi graph G ~ G ( n , 1/2), have been intensely studied. Nevertheless, existing polynomial time algorithms can ...

4 published by ACM
June 2015 STOC '15: Proceedings of the forty-seventh annual ACM symposium on Theory of computing
Publisher: ACM
Citation Count: 9
Downloads (6 Weeks): 6,   Downloads (12 Months): 33,   Downloads (Overall): 212

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Finding cliques in random graphs and the closely related "planted" clique variant, where a clique of size k is planted in a random G(n,1/2) graph, have been the focus of substantial study in algorithm design. Despite much effort, the best known polynomial-time algorithms only solve the problem for k = ...

5 published by ACM
May 2012 STOC '12: Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Publisher: ACM
Citation Count: 1
Downloads (6 Weeks): 1,   Downloads (12 Months): 12,   Downloads (Overall): 291

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We prove tight size bounds on monotone switching networks for the k-clique problem, and for an explicit monotone problem by analyzing the generation problem with a pyramid structure of height h. This gives alternative proofs of the separations of m-NC from m-P and of m-NC i from m-NC i+1 , ...
Keywords: lower bounds, parallel complexity, switching networks, monotone complexity, space complexity

October 2010 FOCS '10: Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science
Publisher: IEEE Computer Society
Citation Count: 4

We prove that any monotone switching network solving directed connectivity on $N$ vertices must have size $N^{\Omega(\log N)}$
Keywords: L, NL, computational complexity, switching networks

March 2008 Designs, Codes and Cryptography: Volume 46 Issue 3, March 2008
Publisher: Kluwer Academic Publishers
Citation Count: 2

We show that there are no complete 44-caps in AG(5, 3). We then use this result to prove that the maximal size for a cap in AG(6, 3) is equal to 112, and that the 112-caps in AG(6, 3) are unique up to affine equivalence.
Keywords: 51E20, 51E22, Coding theory, 05B25, Caps, Finite geometry

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