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Lattice Basis Reduction: Improved Practical Algorithms and Solving Subset Sum Problems.
 Math. Programming
, 1993
"... We report on improved practical algorithms for lattice basis reduction. We propose a practical floating point version of the L3algorithm of Lenstra, Lenstra, Lov'asz (1982). We present a variant of the L3 algorithm with "deep insertions" and a practical algorithm for block KorkinZ ..."
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Cited by 327 (6 self)
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Zolotarev reduction, a concept introduced by Schnorr (1987). Empirical tests show that the strongest of these algorithms solves almost all subset sum problems with up to 66 random weights of arbitrary bit length within at most a few hours on a UNISYS 6000/70 or within a couple of minutes on a SPARC 1+ computer.
Codes and Decoding on General Graphs
, 1996
"... Iterative decoding techniques have become a viable alternative for constructing high performance coding systems. In particular, the recent success of turbo codes indicates that performance close to the Shannon limit may be achieved. In this thesis, it is showed that many iterative decoding algorithm ..."
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Cited by 359 (1 self)
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algorithms are special cases of two generic algorithms, the minsum and sumproduct algorithms, which also include noniterative algorithms such as Viterbi decoding. The minsum and sumproduct algorithms are developed and presented as generalized trellis algorithms, where the time axis of the trellis
Linear Modeling Of mRNA Expression Levels During CNS Development And Injury
, 1999
"... this paper, we will leave out the inputs to these genes. Since the least squares solution essentially solves a linear regression for each gene independently, failure to achieve a biologically plausible model for some of the genes does not imply that the rest of the model is unreliable. The sum of in ..."
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Cited by 239 (3 self)
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this paper, we will leave out the inputs to these genes. Since the least squares solution essentially solves a linear regression for each gene independently, failure to achieve a biologically plausible model for some of the genes does not imply that the rest of the model is unreliable. The sum
Solving lowdensity subset sum problems
 in Proceedings of 24rd Annu. Symp. Foundations of comput. Sci
, 1983
"... Abstract. The subset sum problem is to decide whether or not the O1 integer programming problem C aixi = M, Vi,x,=O or 1, il has a solution, where the ai and M are given positive integers. This problem is NPcomplete, and the difficulty of solving it is the basis of publickey cryptosystems of kna ..."
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Cited by 124 (3 self)
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, and then uses a lattice basis reduction algorithm due to A. K. Lenstra, H. W. Lenstra, Jr., and L. Lovasz to attempt to find v. The performance of the proposed algorithm is analyzed. Let the density d of a subset sum problem be defined by d = n/log2(maxi ai). Then for “almost all ” problems of density d c 0
An improved lowdensity subset sum algorithm
 in Advances in Cryptology: Proceedings of Eurocrypt '91
"... Abstract. The general subset sum problem is NPcomplete. However, there are two algorithms, one due to Brickell and the other to Lagarias and Odlyzko, which in polynomial time solve almost all subset sum problems of sufficiently low density. Both methods rely on basis reduction algorithms to find sh ..."
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Cited by 106 (14 self)
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Abstract. The general subset sum problem is NPcomplete. However, there are two algorithms, one due to Brickell and the other to Lagarias and Odlyzko, which in polynomial time solve almost all subset sum problems of sufficiently low density. Both methods rely on basis reduction algorithms to find
Symmetry Groups, Semidefinite Programs, and Sums of Squares
, 2002
"... We investigate the representation of symmetric polynomials as a sum of squares. Since this task is solved using semidefinite programming tools we explore the geometric, algebraic, and computational implications of the presence of discrete symmetries in semidefinite programs. It is shown that symmetr ..."
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Cited by 100 (14 self)
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that symmetry exploitation allows a significant reduction in both matrix size and number of decision variables. This result is applied to semidefinite programs arising from the computation of sum of squares decompositions for multivariate polynomials. The results, reinterpreted from an invariant
ACONJECTUREOFEVANS ON SUMS OF KLOOSTERMAN SUMS
"... Evans relates twisted Kloosterman sheaf sums to Gaussian hypergeometric functions, and he formulates a number of conjectures relating certain twisted Kloosterman sheaf sums to the coefficients of modular forms. Here we prove one of his conjectures for a fourth order twisted Kloosterman sheaf sum Tn ..."
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of the quadratic character on F × p. In the course of the proof we develop reductions for twisted moments of Kloosterman sums and apply these in the end to derive a congruence relation for Tn with generalized Apéry numbers.
SUM FORMULAS FOR REDUCTIVE ALGEBRAIC GROUPS
, 2006
"... Abstract. Let V be a Weyl module either for a reductive algebraic group G or for the corresponding quantum group Uq. If G is defined over a field of positive characteristic p, respectively if q is a primitive l’th root of unity (in an arbitrary field) then V has a Jantzen filtration V = V 0 ⊃ V 1 · ..."
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Abstract. Let V be a Weyl module either for a reductive algebraic group G or for the corresponding quantum group Uq. If G is defined over a field of positive characteristic p, respectively if q is a primitive l’th root of unity (in an arbitrary field) then V has a Jantzen filtration V = V 0 ⊃ V 1
Determinant sums for undirected hamiltonicity
 in Prof. of FOCS’10, 2010
"... We present a Monte Carlo algorithm for Hamiltonicity detection in an nvertex undirected graph running in O ∗ (1.657 n) time. To the best of our knowledge, this is the first superpolynomial improvement on the worst case runtime for the problem since the O ∗ (2 n) bound established for TSP almost fif ..."
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Cited by 46 (1 self)
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space polynomial in n. We combine several recently resurrected ideas to get the results. Our main technical contribution is a new reduction inspired by the algebraic sieving method for kPath (Koutis ICALP 2008, Williams IPL 2009). We introduce the Labeled Cycle Cover Sum in which weareset tocount
Results 1  10
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1,922