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CORR
2010
Springer
152views Education» more  CORR 2010»
13 years 7 months ago
A Faster Algorithm for Quasi-convex Integer Polynomial Optimization
We present a faster exponential-time algorithm for integer optimization over quasi-convex polynomials. We study the minimization of a quasiconvex polynomial subject to s quasi-con...
Robert Hildebrand, Matthias Köppe
STOC
2007
ACM
85views Algorithms» more  STOC 2007»
14 years 7 months ago
Faster integer multiplication
For more than 35 years, the fastest known method for integer multiplication has been the Sch?onhage-Strassen algorithm running in time O(n log n log log n). Under certain restricti...
Martin Fürer
CRYPTO
2007
Springer
144views Cryptology» more  CRYPTO 2007»
14 years 1 months ago
Finding Small Roots of Bivariate Integer Polynomial Equations: A Direct Approach
Coppersmith described at Eurocrypt 96 an algorithm for finding small roots of bivariate integer polynomial equations, based on lattice reduction. A simpler algorithm was later pro...
Jean-Sébastien Coron
WADS
2009
Springer
226views Algorithms» more  WADS 2009»
14 years 1 months ago
Integer Programming: Optimization and Evaluation Are Equivalent
Abstract We show that if one can find the optimal value of an integer programming problem min{cx : Ax ≥ b, x ∈ Zn +} in polynomial time, then one can find an optimal solution...
James B. Orlin, Abraham P. Punnen, Andreas S. Schu...
IWPEC
2009
Springer
14 years 1 months ago
Even Faster Algorithm for Set Splitting!
In the p-Set Splitting problem we are given a universe U, a family F of subsets of U and a positive integer k and the objective is to find a partition of U into W and B such that...
Daniel Lokshtanov, Saket Saurabh