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COCO
2008
Springer
100views Algorithms» more  COCO 2008»
13 years 8 months ago
Detecting Rational Points on Hypersurfaces over Finite Fields
We study the complexity of deciding whether a given homogeneous multivariate polynomial has a nontrivial root over a finite field. Given a homogeneous algebraic circuit C that com...
Swastik Kopparty, Sergey Yekhanin
COMPGEOM
1997
ACM
13 years 11 months ago
Computing Exact Geometric Predicates Using Modular Arithmetic with Single Precision
Abstract: We propose an e cient method that determines the sign of a multivariate polynomial expression with integer coe cients. This is a central operation on which the robustness...
Hervé Brönnimann, Ioannis Z. Emiris, V...
CORR
2010
Springer
138views Education» more  CORR 2010»
13 years 6 months ago
Shallow Circuits with High-Powered Inputs
A polynomial identity testing algorithm must determine whether an input polynomial (given for instance by an arithmetic circuit) is identically equal to 0. In this paper, we show ...
Pascal Koiran
STOC
1998
ACM
135views Algorithms» more  STOC 1998»
13 years 11 months ago
Checking Polynomial Identities over any Field: Towards a Derandomization?
We present a Monte Carlo algorithm for testing multivariate polynomial identities over any field using fewer random bits than other methods. To test if a polynomial P(x1 ::: xn) ...
Daniel Lewin, Salil P. Vadhan
RSA
2008
123views more  RSA 2008»
13 years 6 months ago
Generating unlabeled connected cubic planar graphs uniformly at random
We present an expected polynomial time algorithm to generate an unlabeled connected cubic planar graph uniformly at random. We first consider rooted connected cubic planar graphs, ...
Manuel Bodirsky, Clemens Gröpl, Mihyun Kang