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Tarjan Transcript Final with Timestamps
A.M. Turing Award Oral History Interview with Robert (Bob) Endre Tarjan by Roy Levin San Mateo, California July 12, 2017 Levin: My name is Roy Levin. Today is July 12th, 2017, and I’m in San Mateo, California at the home of Robert Tarjan, where I’ll be interviewing him for the ACM Turing Award Winners project. Good afternoon, Bob, and thanks for spending the time to talk to me today. Tarjan: You’re welcome. Levin: I’d like to start by talking about your early technical interests and where they came from. When do you first recall being interested in what we might call technical things? Tarjan: Well, the first thing I would say in that direction is my mom took me to the public library in Pomona, where I grew up, which opened up a huge world to me. I started reading science fiction books and stories. Originally, I wanted to be the first person on Mars, that was what I was thinking, and I got interested in astronomy, started reading a lot of science stuff. I got to junior high school and I had an amazing math teacher. His name was Mr. Wall. I had him two years, in the eighth and ninth grade. He was teaching the New Math to us before there was such a thing as “New Math.” He taught us Peano’s axioms and things like that. It was a wonderful thing for a kid like me who was really excited about science and mathematics and so on. The other thing that happened was I discovered Scientific American in the public library and started reading Martin Gardner’s columns on mathematical games and was completely fascinated. -
Donald Knuth Fletcher Jones Professor of Computer Science, Emeritus Curriculum Vitae Available Online
Donald Knuth Fletcher Jones Professor of Computer Science, Emeritus Curriculum Vitae available Online Bio BIO Donald Ervin Knuth is an American computer scientist, mathematician, and Professor Emeritus at Stanford University. He is the author of the multi-volume work The Art of Computer Programming and has been called the "father" of the analysis of algorithms. He contributed to the development of the rigorous analysis of the computational complexity of algorithms and systematized formal mathematical techniques for it. In the process he also popularized the asymptotic notation. In addition to fundamental contributions in several branches of theoretical computer science, Knuth is the creator of the TeX computer typesetting system, the related METAFONT font definition language and rendering system, and the Computer Modern family of typefaces. As a writer and scholar,[4] Knuth created the WEB and CWEB computer programming systems designed to encourage and facilitate literate programming, and designed the MIX/MMIX instruction set architectures. As a member of the academic and scientific community, Knuth is strongly opposed to the policy of granting software patents. He has expressed his disagreement directly to the patent offices of the United States and Europe. (via Wikipedia) ACADEMIC APPOINTMENTS • Professor Emeritus, Computer Science HONORS AND AWARDS • Grace Murray Hopper Award, ACM (1971) • Member, American Academy of Arts and Sciences (1973) • Turing Award, ACM (1974) • Lester R Ford Award, Mathematical Association of America (1975) • Member, National Academy of Sciences (1975) 5 OF 44 PROFESSIONAL EDUCATION • PhD, California Institute of Technology , Mathematics (1963) PATENTS • Donald Knuth, Stephen N Schiller. "United States Patent 5,305,118 Methods of controlling dot size in digital half toning with multi-cell threshold arrays", Adobe Systems, Apr 19, 1994 • Donald Knuth, LeRoy R Guck, Lawrence G Hanson. -
Modified Moments for Indefinite Weight Functions [2Mm] (A Tribute
Modified Moments for Indefinite Weight Functions (a Tribute to a Fruitful Collaboration with Gene H. Golub) Martin H. Gutknecht Seminar for Applied Mathematics ETH Zurich Remembering Gene Golub Around the World Leuven, February 29, 2008 Martin H. Gutknecht Modified Moments for Indefinite Weight Functions My education in numerical analysis at ETH Zurich My teachers of numerical analysis: Eduard Stiefel [1909–1978] (first, basic NA course, 1964) Peter Läuchli [b. 1928] (ALGOL, 1965) Hans-Rudolf Schwarz [b. 1930] (numerical linear algebra, 1966) Heinz Rutishauser [1917–1970] (follow-up numerical analysis course; “selected chapters of NM” [several courses]; computer hands-on training) Peter Henrici [1923–1987] (computational complex analysis [many courses]) The best of all worlds? Martin H. Gutknecht Modified Moments for Indefinite Weight Functions My education in numerical analysis (cont’d) What did I learn? Gauss elimination, simplex alg., interpolation, quadrature, conjugate gradients, ODEs, FDM for PDEs, ... qd algorithm [often], LR algorithm, continued fractions, ... many topics in computational complex analysis, e.g., numerical conformal mapping What did I miss to learn? (numerical linear algebra only) QR algorithm nonsymmetric eigenvalue problems SVD (theory, algorithms, applications) Lanczos algorithm (sym., nonsym.) Padé approximation, rational interpolation Martin H. Gutknecht Modified Moments for Indefinite Weight Functions My first encounters with Gene H. Golub Gene’s first two talks at ETH Zurich (probably) 4 June 1971: “Some modified eigenvalue problems” 28 Nov. 1974: “The block Lanczos algorithm” Gene was one of many famous visitors Peter Henrici attracted. Fall 1974: GHG on sabbatical at ETH Zurich. I had just finished editing the “Lectures of Numerical Mathematics” of Heinz Rutishauser (1917–1970). -
Reducibility
Reducibility t REDUCIBILITY AMONG COMBINATORIAL PROBLEMS Richard M. Karp University of California at Berkeley Abstract: A large class of computational problems involve the determination of properties of graphs, digraphs, integers, arrays of integers, finite families of finite sets, boolean formulas and elements of other countable domains. Through simple encodings from such domains into the set of words over a finite alphabet these problems can be converted into language recognition problems, and we can inquire into their computational complexity. It is reasonable to consider such a problem satisfactorily solved when an algorithm for its solution is found which terminates within a . number of steps bounded by a polynomial in the length of the input. We show that a large number of classic unsolved problems of cover- ing. matching, packing, routing, assignment and sequencing are equivalent, in the sense that either each of them possesses a polynomial-bounded algorithm or none of them does. 1. INTRODUCTION All the general methods presently known for computing the chromatic number of a graph, deciding whether a graph has a Hamilton circuit. or solving a system of linear inequalities in which the variables are constrained to be 0 or 1, require a combinatorial search for which the worst case time requirement grows exponentially with the length of the input. In this paper we give theorems which strongly suggest, but do not imply, that these problems, as well as many others, will remain intractable perpetually. t This research was partially supported by National Science Founda- tion Grant GJ-474. 85 R. E. Miller et al. (eds.), Complexity of Computer Computations © Plenum Press, New York 1972 86 RICHARD M. -
Mathematical Circus & 'Martin Gardner
MARTIN GARDNE MATHEMATICAL ;MATH EMATICAL ASSOCIATION J OF AMERICA MATHEMATICAL CIRCUS & 'MARTIN GARDNER THE MATHEMATICAL ASSOCIATION OF AMERICA Washington, DC 1992 MATHEMATICAL More Puzzles, Games, Paradoxes, and Other Mathematical Entertainments from Scientific American with a Preface by Donald Knuth, A Postscript, from the Author, and a new Bibliography by Mr. Gardner, Thoughts from Readers, and 105 Drawings and Published in the United States of America by The Mathematical Association of America Copyright O 1968,1969,1970,1971,1979,1981,1992by Martin Gardner. All riglhts reserved under International and Pan-American Copyright Conventions. An MAA Spectrum book This book was updated and revised from the 1981 edition published by Vantage Books, New York. Most of this book originally appeared in slightly different form in Scientific American. Library of Congress Catalog Card Number 92-060996 ISBN 0-88385-506-2 Manufactured in the United States of America For Donald E. Knuth, extraordinary mathematician, computer scientist, writer, musician, humorist, recreational math buff, and much more SPECTRUM SERIES Published by THE MATHEMATICAL ASSOCIATION OF AMERICA Committee on Publications ANDREW STERRETT, JR.,Chairman Spectrum Editorial Board ROGER HORN, Chairman SABRA ANDERSON BART BRADEN UNDERWOOD DUDLEY HUGH M. EDGAR JEANNE LADUKE LESTER H. LANGE MARY PARKER MPP.a (@ SPECTRUM Also by Martin Gardner from The Mathematical Association of America 1529 Eighteenth Street, N.W. Washington, D. C. 20036 (202) 387- 5200 Riddles of the Sphinx and Other Mathematical Puzzle Tales Mathematical Carnival Mathematical Magic Show Contents Preface xi .. Introduction Xlll 1. Optical Illusions 3 Answers on page 14 2. Matches 16 Answers on page 27 3. -
Lipics-ISAAC-2020-42.Pdf (0.5
Multiparty Selection Ke Chen Department of Computer Science, University of Wisconsin–Milwaukee, WI, USA [email protected] Adrian Dumitrescu Department of Computer Science, University of Wisconsin–Milwaukee, WI, USA [email protected] Abstract Given a sequence A of n numbers and an integer (target) parameter 1 ≤ i ≤ n, the (exact) selection problem is that of finding the i-th smallest element in A. An element is said to be (i, j)-mediocre if it is neither among the top i nor among the bottom j elements of S. The approximate selection problem is that of finding an (i, j)-mediocre element for some given i, j; as such, this variant allows the algorithm to return any element in a prescribed range. In the first part, we revisit the selection problem in the two-party model introduced by Andrew Yao (1979) and then extend our study of exact selection to the multiparty model. In the second part, we deduce some communication complexity benefits that arise in approximate selection. In particular, we present a deterministic protocol for finding an approximate median among k players. 2012 ACM Subject Classification Theory of computation Keywords and phrases approximate selection, mediocre element, comparison algorithm, i-th order statistic, tournaments, quantiles, communication complexity Digital Object Identifier 10.4230/LIPIcs.ISAAC.2020.42 1 Introduction Given a sequence A of n numbers and an integer (selection) parameter 1 ≤ i ≤ n, the selection problem asks to find the i-th smallest element in A. If the n elements are distinct, the i-th smallest is larger than i − 1 elements of A and smaller than the other n − i elements of A. -
Fundamental Theorems in Mathematics
SOME FUNDAMENTAL THEOREMS IN MATHEMATICS OLIVER KNILL Abstract. An expository hitchhikers guide to some theorems in mathematics. Criteria for the current list of 243 theorems are whether the result can be formulated elegantly, whether it is beautiful or useful and whether it could serve as a guide [6] without leading to panic. The order is not a ranking but ordered along a time-line when things were writ- ten down. Since [556] stated “a mathematical theorem only becomes beautiful if presented as a crown jewel within a context" we try sometimes to give some context. Of course, any such list of theorems is a matter of personal preferences, taste and limitations. The num- ber of theorems is arbitrary, the initial obvious goal was 42 but that number got eventually surpassed as it is hard to stop, once started. As a compensation, there are 42 “tweetable" theorems with included proofs. More comments on the choice of the theorems is included in an epilogue. For literature on general mathematics, see [193, 189, 29, 235, 254, 619, 412, 138], for history [217, 625, 376, 73, 46, 208, 379, 365, 690, 113, 618, 79, 259, 341], for popular, beautiful or elegant things [12, 529, 201, 182, 17, 672, 673, 44, 204, 190, 245, 446, 616, 303, 201, 2, 127, 146, 128, 502, 261, 172]. For comprehensive overviews in large parts of math- ematics, [74, 165, 166, 51, 593] or predictions on developments [47]. For reflections about mathematics in general [145, 455, 45, 306, 439, 99, 561]. Encyclopedic source examples are [188, 705, 670, 102, 192, 152, 221, 191, 111, 635]. -
Purely Functional Data Structures
Purely Functional Data Structures Chris Okasaki September 1996 CMU-CS-96-177 School of Computer Science Carnegie Mellon University Pittsburgh, PA 15213 Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy. Thesis Committee: Peter Lee, Chair Robert Harper Daniel Sleator Robert Tarjan, Princeton University Copyright c 1996 Chris Okasaki This research was sponsored by the Advanced Research Projects Agency (ARPA) under Contract No. F19628- 95-C-0050. The views and conclusions contained in this document are those of the author and should not be interpreted as representing the official policies, either expressed or implied, of ARPA or the U.S. Government. Keywords: functional programming, data structures, lazy evaluation, amortization For Maria Abstract When a C programmer needs an efficient data structure for a particular prob- lem, he or she can often simply look one up in any of a number of good text- books or handbooks. Unfortunately, programmers in functional languages such as Standard ML or Haskell do not have this luxury. Although some data struc- tures designed for imperative languages such as C can be quite easily adapted to a functional setting, most cannot, usually because they depend in crucial ways on as- signments, which are disallowed, or at least discouraged, in functional languages. To address this imbalance, we describe several techniques for designing functional data structures, and numerous original data structures based on these techniques, including multiple variations of lists, queues, double-ended queues, and heaps, many supporting more exotic features such as random access or efficient catena- tion. In addition, we expose the fundamental role of lazy evaluation in amortized functional data structures. -
A Memorable Trip Abhisekh Sankaran Research Scholar, IIT Bombay
A Memorable Trip Abhisekh Sankaran Research Scholar, IIT Bombay It was my first trip to the US. It had not yet sunk in that I had been chosen by ACM India as one of two Ph.D. students from India to attend the big ACM Turing Centenary Celebration in San Francisco until I saw the familiar face of Stephen Cook enter a room in the hotel a short distance from mine; later, Moshe Vardi recognized me from his trip to IITB during FSTTCS, 2011. I recognized Nitin Saurabh from IMSc Chennai, the other student chosen by ACM-India; 11 ACM SIG©s had sponsored students and there were about 75 from all over the world. Registration started at 8am on 15th June, along with breakfast. Collecting my ©Student Scholar© badge and stuffing in some food, I entered a large hall with several hundred seats, a brightly lit podium with a large screen in the middle flanked by two others. The program began with a video giving a brief biography of Alan Turing from his boyhood to the dynamic young man who was to change the world forever. There were inaugural speeches by John White, CEO of ACM, and Vint Cerf, the 2004 Turing Award winner and incoming ACM President. The MC for the event, Paul Saffo, took over and the panel discussions and speeches commenced. A live Twitter feed made it possible for people in the audience and elsewhere to post questions/comments which were actually taken up in the discussions. Of the many sessions that took place in the next two days, I will describe three that I found most interesting. -
An Interview with Donald Knuth 33
Bijlage M An Interview with Donald Knuth 33 An Interview with Donald Knuth DDJ chats with one of the world's leading computer scientists Jack Woehr Dr. Dobb's Journal∗ [email protected] April 1996 For over 25 years, Donald E. Knuth has generally been honorable term, but to some people a computer program- considered one of the world's leading computer scientists. mer is somebody who just follows instructions without un- Although he's authored more than 150 publications, it is derstanding what he's doing, one who just knows how to Knuth's three-volume The Art of Computer Programming get through the idiosyncrasies of some language. which has become a staple on every programmer's book- To me, a computer scientist is somebody who has a way shelf. In 1974, Knuth was the recipient of computer sci- of thinking, which resonates with computer programming. ence's most prestigious prize, the Turing Award. He also The way a computer scientist views knowledge in general received the National Medal of Science in 1979. is different from the way a mathematician views knowl- In addition to his work developing fundamental algorithms edge, which is different from the way a physicist views for computer programming, Knuth was a pioneer in com- knowledge, which is different from the way a chemist, puter typesetting with his TEX, METAFONT, and WEB ap- lawyer, or poet views knowledge. plications. He has written on topics as singular as ancient There's about one person in every ®fty who has this pecu- Babylonian algorithms and has penned a novel. -
COT 5407:Introduction to Algorithms Author and Copyright: Giri Narasimhan Florida International University Lecture 1: August 28, 2007
COT 5407:Introduction to Algorithms Author and Copyright: Giri Narasimhan Florida International University Lecture 1: August 28, 2007. 1 Introduction The field of algorithms is the bedrock on which all of computer science rests. Would you jump into a business project without understanding what is in store for you, without know- ing what business strategies are needed, without understanding the nature of the market, and without evaluating the competition and the availability of skilled available workforce? In the same way, you should not undertake writing a program without thinking out a strat- egy (algorithm), without theoretically evaluating its performance (algorithm analysis), and without knowing what resources you will need and you have available. While there are broad principles of algorithm design, one of the the best ways to learn how to be an expert at designing good algorithms is to do an extensive survey of “case studies”. It provides you with a storehouse of strategies that have been useful for solving other problems. When posed with a new problem, the first step is to “model” your problem appropriately and cast it as a problem (or a variant) that has been previously studied or that can be easily solved. Often the problem is rather complex. In such cases, it is necessary to use general problem-solving techniques that one usually employs in modular programming. This involves breaking down the problem into smaller and easier subproblems. For each subproblem, it helps to start with a skeleton solution which is then refined and elaborated upon in a stepwise manner. Once a strategy or algorithm has been designed, it is important to think about several issues: why is it correct? does is solve all instances of the problem? is it the best possible strategy given the resource limitations and constraints? if not, what are the limits or bounds on the amount of resources used? are improved solutions possible? 2 History of Algorithms It is important for you to know the giants of the field, and the shoulders on which we all stand in order to see far. -
Alan Mathison Turing and the Turing Award Winners
Alan Turing and the Turing Award Winners A Short Journey Through the History of Computer TítuloScience do capítulo Luis Lamb, 22 June 2012 Slides by Luis C. Lamb Alan Mathison Turing A.M. Turing, 1951 Turing by Stephen Kettle, 2007 by Slides by Luis C. Lamb Assumptions • I assume knowlege of Computing as a Science. • I shall not talk about computing before Turing: Leibniz, Babbage, Boole, Gödel... • I shall not detail theorems or algorithms. • I shall apologize for omissions at the end of this presentation. • Comprehensive information about Turing can be found at http://www.mathcomp.leeds.ac.uk/turing2012/ • The full version of this talk is available upon request. Slides by Luis C. Lamb Alan Mathison Turing § Born 23 June 1912: 2 Warrington Crescent, Maida Vale, London W9 Google maps Slides by Luis C. Lamb Alan Mathison Turing: short biography • 1922: Attends Hazlehurst Preparatory School • ’26: Sherborne School Dorset • ’31: King’s College Cambridge, Maths (graduates in ‘34). • ’35: Elected to Fellowship of King’s College Cambridge • ’36: Publishes “On Computable Numbers, with an Application to the Entscheindungsproblem”, Journal of the London Math. Soc. • ’38: PhD Princeton (viva on 21 June) : “Systems of Logic Based on Ordinals”, supervised by Alonzo Church. • Letter to Philipp Hall: “I hope Hitler will not have invaded England before I come back.” • ’39 Joins Bletchley Park: designs the “Bombe”. • ’40: First Bombes are fully operational • ’41: Breaks the German Naval Enigma. • ’42-44: Several contibutions to war effort on codebreaking; secure speech devices; computing. • ’45: Automatic Computing Engine (ACE) Computer. Slides by Luis C.