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» Practical polynomial factoring in polynomial time
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COCO
2009
Springer
128views Algorithms» more  COCO 2009»
15 years 6 months ago
An Almost Optimal Rank Bound for Depth-3 Identities
—We show that the rank of a depth-3 circuit (over any field) that is simple, minimal and zero is at most O(k3 log d). The previous best rank bound known was 2O(k2 ) (log d)k−2...
Nitin Saxena, C. Seshadhri
ISSAC
2005
Springer
115views Mathematics» more  ISSAC 2005»
15 years 5 months ago
Algorithms for the non-monic case of the sparse modular GCD algorithm
Let G = (4y2 + 2z)x2 + (10y2 + 6z) be the greatest common divisor (gcd) of two polynomials A, B ∈   [x,y, z]. Because G is not monic in the main variable x, the sparse modular ...
Jennifer de Kleine, Michael B. Monagan, Allan D. W...
FSTTCS
2010
Springer
14 years 9 months ago
Finding Independent Sets in Unions of Perfect Graphs
ABSTRACT. The maximum independent set problem (MAXIS) on general graphs is known to be NPhard to approximate within a factor of n1-, for any > 0. However, there are many "...
Venkatesan T. Chakaravarthy, Vinayaka Pandit, Samb...
IPCO
2007
126views Optimization» more  IPCO 2007»
15 years 1 months ago
The Smoothed Number of Pareto Optimal Solutions in Bicriteria Integer Optimization
Abstract. A well established heuristic approach for solving various bicriteria optimization problems is to enumerate the set of Pareto optimal solutions, typically using some kind ...
René Beier, Heiko Röglin, Berthold V&o...
PKC
2011
Springer
197views Cryptology» more  PKC 2011»
14 years 2 months ago
Cryptanalysis of Multivariate and Odd-Characteristic HFE Variants
We investigate the security of a generalization of HFE (multivariate and odd-characteristic variants). First, we propose an improved version of the basic Kipnis-Shamir key recovery...
Luk Bettale, Jean-Charles Faugère, Ludovic ...