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CORR
2010
Springer
152views Education» more  CORR 2010»
14 years 10 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»
15 years 10 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»
15 years 4 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»
15 years 4 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
15 years 4 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