Book ChapterDOI
Probabilistic algorithms for sparse polynomials
Richard Zippel
- pp 216-226
TLDR
This work has tried to demonstrate how sparse techniques can be used to increase the effectiveness of the modular algorithms of Brown and Collins and believes this work has finally laid to rest the bad zero problem.Abstract:
In this paper we have tried to demonstrate how sparse techniques can be used to increase the effectiveness of the modular algorithms of Brown and Collins. These techniques can be used for an extremely wide class of problems and can applied to a number of different algorithms including Hensel's lemma. We believe this work has finally laid to rest the bad zero problem.read more
Citations
More filters
Book
Randomized Algorithms
TL;DR: This book introduces the basic concepts in the design and analysis of randomized algorithms and presents basic tools such as probability theory and probabilistic analysis that are frequently used in algorithmic applications.
Proceedings ArticleDOI
Ciphertext-Policy Attribute-Based Encryption
TL;DR: A system for realizing complex access control on encrypted data that is conceptually closer to traditional access control methods such as role-based access control (RBAC) and secure against collusion attacks is presented.
Book
Structure and Interpretation of Computer Programs
TL;DR: Structure and Interpretation of Computer Programs emphasizes the central role played by different approaches to dealing with time in computational models, appropriate for an introduction to computer science courses, as well as programming languages and program design.
Book
Parameterized Algorithms
Marek Cygan,Fedor V. Fomin,Lukasz Kowalik,Daniel Lokshtanov,Dániel Marx,Marcin Pilipczuk,Michał Pilipczuk,Saket Saurabh +7 more
TL;DR: This comprehensive textbook presents a clean and coherent account of most fundamental tools and techniques in Parameterized Algorithms and is a self-contained guide to the area, providing a toolbox of algorithmic techniques.
Journal ArticleDOI
The NP-completeness column: An ongoing guide
TL;DR: This is the fourteenth edition of a quarterly column that provides continuing coverage of new developments in the theory of NP-completeness, and readers who have results they would like mentioned (NP-hardness, PSPACE- hardness, polynomialtime-solvability, etc.), or open problems they wouldlike publicized, should send them to David S. Johnson.
References
More filters
Journal ArticleDOI
A Fast Monte-Carlo Test for Primality
Robert Solovay,Volker Strassen +1 more
TL;DR: A uniform distribution a from a uniform distribution on the set 1, 2, 3, 4, 5 is a random number and if a and n are relatively prime, compute the residue varepsilon.
Journal ArticleDOI
On Euclid's Algorithm and the Computation of Polynomial Greatest Common Divisors
TL;DR: This paper examines the computation of polynomial greatest common divisors by various generalizations of Euclid's algorithm, and it is shown that the modular algorithm is markedly superior.
Journal ArticleDOI
On Hensel factorization, I
TL;DR: In this article, a padic method for the constructive factorization of monic polynomials over a dedekind ring o and the ideal theory of o [x] are developed.
Journal ArticleDOI
An improved multivariate polynomial factoring algorithm
TL;DR: A new algorithm for factoring multivariate polynomials over the integers based on an algorithm by Wang and Rothschild is described, which is generally faster and requires less store then the original algorithm.