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VC
2008
102views more  VC 2008»
13 years 7 months ago
Solving nonlinear polynomial systems in the barycentric Bernstein basis
We present a method for solving arbitrary systems of N nonlinear polynomials in n variables over an n-dimensional simplicial domain based on polynomial representation in the baryce...
Martin Reuter, Tarjei S. Mikkelsen, Evan C. Sherbr...
STOC
2009
ACM
119views Algorithms» more  STOC 2009»
14 years 8 months ago
Explicit construction of a small epsilon-net for linear threshold functions
We give explicit constructions of epsilon nets for linear threshold functions on the binary cube and on the unit sphere. The size of the constructed nets is polynomial in the dime...
Yuval Rabani, Amir Shpilka
FOCS
1992
IEEE
13 years 11 months ago
Maximizing Non-Linear Concave Functions in Fixed Dimension
Consider a convex set P in IRd and a piecewise polynomial concave function F: P IR. Let A be an algorithm that given a point x IRd computes F(x) if x P, or returns a concave po...
Sivan Toledo
DAM
2010
112views more  DAM 2010»
13 years 7 months ago
New results on optimizing rooted triplets consistency
Abstract. A set of phylogenetic trees with overlapping leaf sets is consistent if it can be merged without conflicts into a supertree. In this paper, we study the polynomial-time a...
Jaroslaw Byrka, Sylvain Guillemot, Jesper Jansson
JACM
2000
119views more  JACM 2000»
13 years 7 months ago
A subdivision-based algorithm for the sparse resultant
Multivariate resultants generalize the Sylvester resultant of two polynomials and characterize the solvability of a polynomial system. They also reduce the computation of all comm...
John F. Canny, Ioannis Z. Emiris