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CORR
2010
Springer

A Faster Algorithm for Quasi-convex Integer Polynomial Optimization

14 years 16 days 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-convex polynomial constraints and integrality constraints for all variables. The new algorithm is an improvement upon the best known algorithm due to Heinz (Journal of Complexity, 2005). A lower time complexity is reached through applying a stronger ellipsoid rounding method and applying a recent advancement in the shortest vector problem to give a smaller exponential-time complexity of a Lenstra-type algorithm. For the bounded case, our algorithm attains a time-complexity of s(rlMd)O(1) 22n log2(n)+O(n) when M is a bound on the number of monomials in each polynomial and r is the binary encoding length of a bound on the feasible region. In the general case, slO(1) dO(n) 22n log2(n) . In each we assume d 2 is a bound on the total degree of the polynomials and l bounds the maximum binary encoding size of the inpu...
Robert Hildebrand, Matthias Köppe
Added 09 Dec 2010
Updated 09 Dec 2010
Type Journal
Year 2010
Where CORR
Authors Robert Hildebrand, Matthias Köppe
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