Approximate Polynomial gcd: Small Degree and Small Height Perturbations

We consider the following computational problem: we are given two coprime univariate polynomials f 0 and f 1 over a ring \(\mathcal{R}\) and want to find whether after a small perturbation we can achieve a large gcd. We solve this problem in polynomial ti

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Editorial Board David Hutchison Lancaster University, UK Takeo Kanade Carnegie Mellon University, Pittsburgh, PA, USA Josef Kittler University of Surrey, Guildford, UK Jon M. Kleinberg Cornell University, Ithaca, NY, USA Alfred Kobsa University of California, Irvine, CA, USA Friedemann Mattern ETH Zurich, Switzerland John C. Mitchell Stanford University, CA, USA Moni Naor Weizmann Institute of Science, Rehovot, Israel Oscar Nierstrasz University of Bern, Switzerland C. Pandu Rangan Indian Institute of Technology, Madras, India Bernhard Steffen University of Dortmund, Germany Madhu Sudan Massachusetts Institute of Technology, MA, USA Demetri Terzopoulos University of California, Los Angeles, CA, USA Doug Tygar University of California, Berkeley, CA, USA Gerhard Weikum Max-Planck Institute of Computer Science, Saarbruecken, Germany

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Eduardo Sany Laber Claudson Bornstein Loana Tito Nogueira Luerbio Faria (Eds.)

LATIN 2008: Theoretical Informatics 8th Latin American Symposium Búzios, Brazil, April 7-11, 2008 Proceedings

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Volume Editors Eduardo Sany Laber PUC-RIO Departamento de Informática RDC ANDAR 5, Rua Marques de São Vicente, Gávea, Brazil E-mail: [email protected] Claudson Bornstein Universidade Federal do Rio de Janeiro Departamento de Ciência da Computação 21941-590, Rio de Janeiro, RJ, Brazil E-mail: [email protected] Loana Tito Nogueira Universidade Federal Fluminense Instituto de Computação Rua Passo da Patria 156, 24210-240, São Domingos, Niterói, RJ, Brazil E-mail: [email protected] Luerbio Faria Universidade Estadual do Rio de Janeiro Rua Dr. Francisco Portela, 24435-005, São Gonçalo, RJ, Brazil E-mail: [email protected]

Library of Congress Control Number: 2008922953 CR Subject Classification (1998): F.2, F.1, E.1, E.3, G.2, G.1, I.3.5, F.3, F.4 LNCS Sublibrary: SL 1 – Theoretical Computer Science and General Issues ISSN ISBN-10 ISBN-13

0302-9743 3-540-78772-0 Springer Berlin Heidelberg New York 978-3-540-78772-3 Springer Berlin Heidelberg New York

This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. Springer is a part of Springer Science+Business Media springer.com © Springer-Verlag Berlin Heidelberg 2008 Printed in Germany Typesetting: Camera-ready by author, data conversion by Scientific Publishing Services, Chennai, India Printed on acid-free paper SPIN: 12244744 06/3180 543210

Preface

The Latin American Theoretical INformatics Symposium (LATIN) is becoming a traditional and high-quality conference on the Theory of Computing. Previous conferences have been o