Results 1 - 10 of 4,651

On the Asymptotic Complexity of Solving LWE

by Gottfried Herold, Elena Kirshanova, Er May
"... Abstract. We provide for the first time an asymptotic comparison of all known algorithms for the search version of the Learning with Errors (LWE) problem. This includes an analysis of several lattice-based approaches as well as the com-binatorial BKW algorithm. Our analysis of the lattice-based appr ..."
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-based approaches defines a general framework, in which the algorithms of Babai, Lindner-Peikert and several pruning strategies appear as special cases. We show that within this framework, all lattice algorithms achieve the same asymptotic complexity. For the BKW algorithm, we present a refined analysis

Generalised entropy and asymptotic complexities of languages

by Yuri Kalnishkan, Michael V. Vyugin, Vladimir Vovk - In 20th Annual Conference on Learning Theory, COLT 2007 , 2007
"... The paper explores connections between asymptotic complexity and generalised entropy. Asymptotic complexity of a language (a lan-guage is a set of finite or infinite strings) is a way of formalising the complexity of predicting the next element in a sequence: it is the loss per element of a strategy ..."
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The paper explores connections between asymptotic complexity and generalised entropy. Asymptotic complexity of a language (a lan-guage is a set of finite or infinite strings) is a way of formalising the complexity of predicting the next element in a sequence: it is the loss per element of a

The Asymptotic Complexity of Merging Networks

by Peter Bro Miltersen, Mike Paterson, Jun Tarui, Coventry Cv Al - In Proc. 33rd IEEE-FOCS , 1992
"... Let M (m; n) be the minimum number of comparators needed in a comparator network that merges m elements x 1 x 2 : : : xm and n elements y 1 y 2 : : : y n , where n m. Batcher's odd-even merge yields the following upper bound: M (m; n) 1 2 (m + n) log 2 m +O(n); in particular, M (n; n ..."
Abstract - Cited by 8 (0 self) - Add to MetaCart
; n) n log 2 n + O(n): We prove the following lower bound that matches the upper bound above asymptotically as n m !1: M (m; n) 1 2 (m + n) log 2 m \Gamma O(m); in particular, M (n; n) n log 2 n \Gamma O(n): Our proof technique extends to give similarly tight lower bounds for the size

Asymptotic Complexity in Filtration Equations

by J. A. Carrillo, J. L. Vázquez , 2006
"... We show that the solutions of nonlinear diffusion equations of the form ut = ∆Φ(u) appearing in filtration theory may present complicated asymptotics as t → ∞ whenever we alternate infinitely many times in a suitable manner the behavior of the nonlinearity Φ. Oscillatory behaviour is demonstrated f ..."
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We show that the solutions of nonlinear diffusion equations of the form ut = ∆Φ(u) appearing in filtration theory may present complicated asymptotics as t → ∞ whenever we alternate infinitely many times in a suitable manner the behavior of the nonlinearity Φ. Oscillatory behaviour is demonstrated

The Asymptotic Complexity of Partial Sorting

by Jobst Heitzig
"... The expected number of pairwise comparisons needed to learn a partial order on n elements is shown to be at least n^2/4 + o(n^2), and an algorithm is given that needs only n^2/4 + o(n^2) comparisons on average. In addition, the optimal strategy for learning a poset with four elements is presented. ..."
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The expected number of pairwise comparisons needed to learn a partial order on n elements is shown to be at least n^2/4 + o(n^2), and an algorithm is given that needs only n^2/4 + o(n^2) comparisons on average. In addition, the optimal strategy for learning a poset with four elements is presented.

Singular Combinatorics

by Philippe Flajolet - ICM 2002 VOL. III 1-3 , 2002
"... Combinatorial enumeration leads to counting generating functions presenting a wide variety of analytic types. Properties of generating functions at singularities encode valuable information regarding asymptotic counting and limit probability distributions present in large random structures. " ..."
Abstract - Cited by 800 (10 self) - Add to MetaCart
. "Singularity analysis" reviewed here provides constructive estimates that are applicable in several areas of combinatorics. It constitutes a complex-analytic Tauberian procedure by which combinatorial constructions and asymptotic-probabilistic laws can be systematically related.

Depth-first Iterative-Deepening: An Optimal Admissible Tree Search

by Richard E. Korf - Artificial Intelligence , 1985
"... The complexities of various search algorithms are considered in terms of time, space, and cost of solution path. It is known that breadth-first search requires too much space and depth-first search can use too much time and doesn't always find a cheapest path. A depth-first iteratiw-deepening a ..."
Abstract - Cited by 527 (24 self) - Add to MetaCart
The complexities of various search algorithms are considered in terms of time, space, and cost of solution path. It is known that breadth-first search requires too much space and depth-first search can use too much time and doesn't always find a cheapest path. A depth-first iteratiw

Points-to Analysis in Almost Linear Time

by Bjarne Steensgaard , 1996
"... We present an interprocedural flow-insensitive points-to analysis based on type inference methods with an almost linear time cost complexity. To our knowledge, this is the asymptotically fastest non-trivial interprocedural points-to analysis algorithm yet described. The algorithm is based on a non-s ..."
Abstract - Cited by 595 (3 self) - Add to MetaCart
We present an interprocedural flow-insensitive points-to analysis based on type inference methods with an almost linear time cost complexity. To our knowledge, this is the asymptotically fastest non-trivial interprocedural points-to analysis algorithm yet described. The algorithm is based on a non

Factoring wavelet transforms into lifting steps

by Ingrid Daubechies, Wim Sweldens - J. FOURIER ANAL. APPL , 1998
"... This paper is essentially tutorial in nature. We show how any discrete wavelet transform or two band subband filtering with finite filters can be decomposed into a finite sequence of simple filtering steps, which we call lifting steps but that are also known as ladder structures. This decompositio ..."
Abstract - Cited by 584 (8 self) - Add to MetaCart
in the biorthogonal, i.e, non-unitary case. Like the lattice factorization, the decomposition presented here asymptotically reduces the computational complexity of the transform by a factor two. It has other applications, such as the possibility of defining a wavelet-like transform that maps integers to integers.

THE ASYMPTOTIC COMPLEXITY OF MATRIX REDUCTION OVER FINITE FIELDS

by Demetres Christofides
"... Abstract. Consider an invertible n × n matrix over some field. The Gauss-Jordan elimination reduces this matrix to the identity matrix using at most n2 row operations and in general that many operations might be needed. In [1] the authors considered matrices in GL(n, q), the set of n × n invertible ..."
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matrices in the finite field of q elements, and provided an al-gorithm using only row operations which performs asymptotically bet-ter than the Gauss-Jordan elimination. More specifically their ‘striped elimination algorithm ’ has asymptotic complexity n 2 logq n
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