Lecture Notes in Computer Science 2292 Edited by G. Goos, J. Hartmanis, and J. van Leeuwen

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1 Lecture Notes in Computer Science 2292 Edited by G. Goos, J. Hartmanis, and J. van Leeuwen

2 3 Berlin Heidelberg New York Barcelona Hong Kong London Milan Paris Tokyo

3 Gholamreza B. Khosrovshahi Ali Shokoufandeh Amin Shokrollahi (Eds.) Theoretical Aspects of Computer Science Advanced Lectures 13

4 Series Editors Gerhard Goos, Karlsruhe University, Germany Juris Hartmanis, Cornell University, NY, USA Jan van Leeuwen, Utrecht University, The Netherlands Volume Editors Gholamreza B. Khosrovshahi Institute for Studies in Theoretical Physics and Mathematics (IPM) Tehran, Iran Ali Shokoufandeh Drexel University, Dept. of Mathematics & Computer Science Philadelphia, PA 19104, USA Amin Shokrollahi Digital Fountain, Inc Civic Center Drive, Fremont, CA 94538, USA Cataloging-in-Publication Data applied for Die Deutsche Bibliothek - CIP-Einheitsaufnahme Theoretical aspects of computer science : advanced lectures / Gholamrez B. Khosrovshahi... (ed.). - Berlin ; Heidelberg ; New York ; Barcelona ; Hong Kong ; London ; Milan ; Paris ; Tokyo : Springer, 2002 (Lecture notes in computer science ; 2292) ISBN CR Subject Classification (1998): G.2, F.2, F.1, C.2, E.1, I.3.5 ISSN ISBN Springer-Verlag 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-Verlag. Violations are liable for prosecution under the German Copyright Law. Springer-Verlag Berlin Heidelberg New York a member of BertelsmannSpringer Science+Business Media GmbH Springer-Verlag Berlin Heidelberg 2002 Printed in Germany Typesetting: Camera-ready by author, data conversion by PTP-Berlin, Stefan Sossna Printed on acid-free paper SPIN: /

5 Preface The First Summer School on Theoretical Aspects on Computer Science was held at the Institute for Studies in Theoretical Physics and Mathematics (IPM) from July 3-10, The idea of organizing a summer school was originated during a conversation between the first and the second editor of this volume in the winter of 2000 at IPM in Tehran. The decision was formalized when the third editor visited IPM later in the winter. The main idea behind the Summer School was to introduce to the students in Iran some of the highly innovative and promising research in Theoretical Computer Science, and, at the same time, to start a flow of ideas between top researchers in the field and the Iranian scientists. For this reason, the talks were designed to be of a tutorial style. The organizers decided to concentrate on a few important areas of research in modern Theoretical Computer Science. To attract students to this important area, they also decided to include talks on applications of methods from Theoretical Computer Science to other areas. This volume contains the written contributions to the program of this Summer School. It is intended for students and researchers who want to gain acquaintance with certain topics in Theoretical Computer Science. The papers on quantum computation, approximation algorithms, self-testing/correcting, algebraic modeling of data, and the Regularity Lemma correspond to the former category, while connections between multiple access communication and combinatorial designs, graph-theoretical methods in computer vision, and low-density parity-check codes belong to the latter category. Each contribution to this volume was presented in a two hour session, leaving ample time for questions and discussions. The tutorials were followed by a number of specialized talks touching on current research problems in the area. Parts of the talks have been incorporated into the material of the contributions. January 2002 G.B. Khosrovshahi A. Shokoufandeh A. Shokrollahi

6 Organization The first International Summer School on Theoretical Aspects of Computer Science was organized by the Institute for Studies in Theoretical Physics and Mathematics (IPM) in Tehran,Iran. Program Committee Conference Chair: Local Arrangements: s# Sponsoring Institutions G. B. Khosrovshahi,IPM and the University of Tehran,Iran A. Shokoufandeh,Drexel University,USA A. Shokrollahi,Digital Fountain,USA M. Zamani School of Mathematics,Institute for Studies in Theoretical Physics and Mathematics (IPM),Tehran,Iran World Mathematical Year (WMY) 2000 National Commission Service de Coopération et d Action Culturelle,Ambassade de France en Iran Neda Rayaneh Institute (NRI)

7 VIII Acknowledgements We are grateful to Professor M. J. Larijani,the director of IPM,who has been a great advocate for the expansion of Theoretical Computer Science at the Institute,and helped us secure major funding from IPM. We would also like to express our thanks to Professor S. Shahshahani,the Deputy Director of IPM, who was most helpful in soliciting financial support from the World Mathematical Year 2000 National Commission. The Service de Coopération et d Action Culturelle of the French embassy in Iran kindly provided travel funds for our invited speakers from France. We thank the Service Culturelle for their generous support. Finally,we would like to express our gratitude to M. Zamani,the executive officer of the School of Mathematics,who single-handedly assumed almost all the responsibilities for the local arrangements of the summer school,and was crucial in making the summer school a successful event.

8 Table of Contents Multiple Access Communications Using Combinatorial Designs... 1 Charles J. Colbourn Exact and Approximate Testing/Correcting of Algebraic Functions: A Survey Marcos Kiwi, Frédéric Magniez, Miklos Santha The RegularityLemma and Its Applications in Graph Theory János Komlós, Ali Shokoufandeh, Miklós Simonovits, Endre Szemerédi Modeling Data and Objects: An Algebraic View Point Kazem Lellahi Graph-Theoretical Methods in Computer Vision Ali Shokoufandeh, Sven Dickinson An Introduction to Low-DensityParity-Check Codes Amin Shokrollahi Primal-Dual Schema Based Approximation Algorithms Vijay V. Vazirani Fourier Transforms and Quantum Computation Umesh Vazirani Author Index...221

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