Algorithms for competitive division of chores

S Brânzei, F Sandomirskiy - arXiv preprint arXiv:1907.01766, 2019 - arxiv.org
We study the problem of allocating divisible bads (chores) among multiple agents with
additive utilities when monetary transfers are not allowed. The competitive rule is known for …

Probabilistic algorithm for polynomial optimization over a real algebraic set

A Greuet, M Safey El Din - SIAM Journal on Optimization, 2014 - SIAM
Let f,f_1,...,f_s be n-variate polynomials with rational coefficients of maximum degree D and
let V be the set of common complex solutions of F=(f_1,...,f_s). We give an algorithm which …

On the geometry of polar varieties

B Bank, M Giusti, J Heintz, M Safey El Din… - Applicable Algebra in …, 2010 - Springer
We have developed in the past several algorithms with intrinsic complexity bounds for the
problem of point finding in real algebraic varieties. Our aim here is to give a comprehensive …

Variant quantifier elimination

H Hong, MS El Din - Journal of Symbolic Computation, 2012 - Elsevier
We describe an algorithm (VQE) for a variant of the real quantifier elimination problem (QE).
The variant problem requires the input to satisfy a certain extra condition, and allows the …

The Voronoi diagram of three lines

H Everett, S Lazard, D Lazard, MS El Din - Proceedings of the twenty …, 2007 - dl.acm.org
We give a complete description of the Voronoi diagram of three lines in R3. In particular, we
show that the topology of the Voronoi diagram is invariant for three lines in general position …

Jacobi stability analysis for systems of ODEs using symbolic computation

B Huang, D Wang, J Yang - … of the 2024 International Symposium on …, 2024 - dl.acm.org
The classical theory of Kosambi–Cartan–Chern (KCC) developed in differential geometry
provides a powerful method for analyzing the behaviors of dynamical systems. In the KCC …

Classification of the perspective-three-point problem, discriminant variety and real solving polynomial systems of inequalities

JC Faugère, G Moroz, F Rouillier… - Proceedings of the twenty …, 2008 - dl.acm.org
Classifying the Perspective-Three-Point problem (abbreviated by P3P in the sequel)
consists in determining the number of possible positions of a camera with respect to the …

Thirty years of Polynomial System Solving, and now?

D Lazard - Journal of symbolic computation, 2009 - Elsevier
Journal of Symbolic Computation Thirty years of Polynomial System Solving, and now? Page 1
Journal of Symbolic Computation 44 (2009) 222–231 Contents lists available at ScienceDirect …

Critical points and Gröbner bases: the unmixed case

JC Faugère, MS El Din, PJ Spaenlehauer - Proceedings of the 37th …, 2012 - dl.acm.org
We consider the problem of computing critical points of the restriction of a polynomial map to
an algebraic variety. This is of first importance since the global minimum of such a map is …

Computing the global optimum of a multivariate polynomial over the reals

MS El Din - Proceedings of the twenty-first international symposium …, 2008 - dl.acm.org
Let f be a polynomial in Q [X1,..., Xn] of degree D. We provide an efficient algorithm in
practice to compute the global supremum supx∈ Rn f (x) of f (or its infimum inf {x∈ Rn} f (x)) …