AMS SHORT COURSE LECTURE NOTES Introductory Survey Lectures

A Subseries of Proceedings of Symposia in Applied Mathematics

Volume 21 MATHEMATICAL ASPECTS OF PRODUCTION AND DISTRIBUTION OF ENERGY Edited by P. D. Lax (San Antonio, Texas, January 1976)

Volume 22 NUMERICAL ANALYSIS Edited by G. H. Golub and J. Oliger (Atlanta, Georgia, January 1978)

Volume 23 MODERN STATISTICS: METHODS AND APPLICATIONS Edited by R. V. Hogg (San Antonio, Texas, January 1980)

Volume 24 GAME THEORY AND ITS APPLICATIONS Edited by W. F. Lucas (Biloxi, Mississippi, January 1979)

Volume 25 OPERATIONS RESEARCH: MATHEMATICS AND MODELS Edited by S. I. Gass (Duluth, Minnesota, August 1979)

Volume 26 THE MATHEMATICS OF NETWORKS Edited by S. A. Burr (Pittsburgh, Pennsylvania, August 1981)

Volume 27 COMPUTED TOMOGRAPHY Edited by L. A. Shepp (Cincinnati, Ohio, January 1982)

Volume 28 STATISTICAL DATA ANALYSIS Edited by R. Gnanadesikan (Toronto, Ontario, August 1982)

Volume 29 APPLIED CRYPTOLOGY, CRYPTOGRAPHIC PROTOCOLS, AND COMPUTER SECURITY MODELS By R. A. DeMillo, G. I. Davida, D. P. Dobkin, M. A. Harrison, and R. J. Lipton

(San Francisco, California, January 1981)

Volume 30 POPULATION BIOLOGY Edited by Simon A. Levin (Albany, New York, August 1983)

Volume 31 COMPUTER COMMUNICATIONS Edited by B. Gopinath (Denver, Colorado, January 1988)

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Volume 33 FAIR ALLOCATION Edited by H Peyton Young (Anaheim, California, January 1985)

http://dx.doi.org/10.1090/psapm/034

AMS SHORT COURSE LECTURE NOTES Introductory Survey Lectures

published as a subseries of Proceedings of Symposia in Applied Mathematics

PROCEEDINGS OF SYMPOSIA IN APPLIED MATHEMATICS

Volume 34

Mathematic s of Informatio n Processin g

Michae l Anshe l an d Willia m Gewirtz , Editor s

American Mathematical Society Providence, Rhode Island

LECTURE NOTES PREPARED FOR THE AMERICAN MATHEMATICAL SOCIETY SHORT COURSE

MATHEMATICS OF INFORMATION PROCESSING

HELD IN LOUISVILLE, KENTUCKY JANUARY 23-24 , 1984

The AMS Short Course Series is sponsored by the Society's Committee on Employment and Education Policy (CEEP). The series is under the direction of the Short Course Advisory Subcommittee of CEEP.

Library of Congress Cataloging in Publication Data Main entry under title:

Mathematics of information processing. (Proceedings of symposia in applied mathematics, ISSN 0160-7634; v. 34) Bibliography: p. Contents: Diameters of communication networks / F. R. K. Chung-The theory of data

dependencies / Ronald Fagin and Moshe Y. Vardi-Transaction management / Hector Garcia-Molina-[etc] 1. Electronic data processing-Mathematics-Congresses. I. Anshel, Michael, 1941 - . II. Gewirtz, William, 1948- . III. Series. QA76.9.M35M39 1986 005.7 85-26693 ISBN 0-8218-0086-8 (alk. paper)

COPYING AND REPRINTING. Individual readers of this publication, and nonprofit libraries acting for them, are permitted to make fair use of the material, such as to copy an article for use in teaching or research. Permission is granted to quote brief passages from this publication in reviews, provided the customary acknowledgment of the source is given.

Republication, systematic copying, or multiple reproduction of any material in this publication (including abstracts) is permitted only under license from the American Math­ematical Society. Requests for such permission should be addressed to the Executive Director, American Mathematical Society, P.O. Box 6248, Providence, Rhode Island 02940.

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1980 Mathematics Subject Classification (1985 Revision). Primary 68-06. Copyright © 1986 by the American Mathematical Society. All rights reserved.

Printed in the United States of America. This volume was printed directly from copy prepared by the authors.

The paper used in this book is acid-free and falls within the guidelines established to ensure permanence and durability.

CONTENTS

List of contributors ix Preface xi Diameters of communication networks

F. R. CHUNG 1

The theory of data dependencies—a survey RONALD FAGIN and MOSHE Y. VARDI 19

Transaction management HECTOR GARCIA-MOLINA 73

Fundamental database issues BARRY E. JACOBS 91

Data compression algorithms VICTOR S.MILLER 107

Application of category theory of structural sets to modelling of information bases of systems

AUGUSTIN A. TUZHILIN 119

v i i

CONTRIBUTORS

F. R. CHUNG, Bell Laboratories, Murray Hill, New Jersey.

RONALD FAGIN, IBM Research Laboratory, San Jose, California.

HECTOR GARCIA-MOLINA, Department of Electrical Engineering and Computer Science, Princeton University, Princeton, New Jersey.

BARRY E. JACOBS, Department of Computer Science, University of Maryland, College Park, Maryland and National Aeronautics and Space Administration, Goddard Space Flight Center, Greenbelt, Maryland.

VICTOR S. MILLER, IBM Watson Research Center, Yorktown Heights, New York.

AUGUSTIN A. TUZHILIN, Department of Computer Science, College of Staten Island, Staten Island, New York.

MOSHE E. VARDI, IBM Research Laboratory, San Jose, California.

ix

PREFACE

This volume contains the lecture notes prepared by six speakers for

the American Mathematical Society Short Course on the Mathematics of Infor­

mation Processing given in Louisville, Kentucky, January 23-24, 1984. The

Short Course Advisory Subcommittee of the AMS approved this concept and

recommended publication of these lecture notes.

The Mathematics of Information Processing is not a single topic but

rather a collection of methodologies whose end-goal is the creation of

automated information systems.

The viewpoint represented here is largely that of American researchers

with heavy emphasis on the mathematical problems of database systems and

communication networks. This reflects the rapid introduction of the products

of information technology in the workplace and in the home. By way of con­

trast a systems-theoretic approach developed in the Soviet Union is included

which also provides a self-contained background should the reader care to

probe more deeply into the subject.

The idea for the Short Course arose while one of us (Anshel) was a

NASA-ASEE Summer Faculty Fellow at Goddard Space Flight Center, NASA. There

we learned of a proposed futuristic information system, IESIS (Intelligent

Earth sensing Information System). The real-world implementation of the

Short Course rested on the shoulders of the practitioner among us (Gewirtz)

who also chaired a lively panel discussion with a surprise guest (Bob Targan).

We would like to thank the speakers for their efforts in the preparation

of these lectures and their patience concerning the idiosyncracies of the

co-director.

Finally we also wish to thank Stefan Burr who acted as wise counsel and

enthusiastic supporter.

Michael Anshel William Gewirtz

City College of the ATT Communications

City University of New York Basking Ridge, New Jersey

xi