Algorithms and Complexity Internet Edition, Summer, 1994
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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. -
Algorithms, Searching and Sorting
Python for Data Scientists L8: Algorithms, searching and sorting 1 Iterative and recursion algorithms 2 Iterative algorithms • looping constructs (while and for loops) lead to iterative algorithms • can capture computation in a set of state variables that update on each iteration through loop 3 Iterative algorithms • “multiply x * y” is equivalent to “add x to itself y times” • capture state by • result 0 • an iteration number starts at y y y-1 and stop when y = 0 • a current value of computation (result) result result + x 4 Iterative algorithms def multiplication_iter(x, y): result = 0 while y > 0: result += x y -= 1 return result 5 Recursion The process of repeating items in a self-similar way 6 Recursion • recursive step : think how to reduce problem to a simpler/smaller version of same problem • base case : • keep reducing problem until reach a simple case that can be solved directly • when y = 1, x*y = x 7 Recursion : example x * y = x + x + x + … + x y items = x + x + x + … + x y - 1 items = x + x * (y-1) Recursion reduction def multiplication_rec(x, y): if y == 1: return x else: return x + multiplication_rec(x, y-1) 8 Recursion : example 9 Recursion : example 10 Recursion : example 11 Recursion • each recursive call to a function creates its own scope/environment • flow of control passes back to previous scope once function call returns value 12 Recursion vs Iterative algorithms • recursion may be simpler, more intuitive • recursion may be efficient for programmer but not for computers def fib_iter(n): if n == 0: return 0 O(n) elif n == 1: return 1 def fib_recur(n): else: if n == 0: O(2^n) a = 0 return 0 b = 1 elif n == 1: for i in range(n-1): return 1 tmp = a else: a = b return fib_recur(n-1) + fib_recur(n-2) b = tmp + b return b 13 Recursion : Proof by induction How do we know that our recursive code will work ? → Mathematical Induction To prove a statement indexed on integers is true for all values of n: • Prove it is true when n is smallest value (e.g. -
Decomposition, Abstraction, Functions
SEARCHING AND SORTING ALGORITHMS 6.00.01X LECTURE 1 SEARCH ALGORITHMS . search algorithm – method for finding an item or group of items with specific properties within a collection of items . collection could be implicit ◦ example – find square root as a search problem ◦ exhaustive enumeration ◦ bisection search ◦ Newton-Raphson . collection could be explicit ◦ example – is a student record in a stored collection of data? SEARCHING ALGORITHMS . linear search • brute force search • list does not have to be sorted . bisection search • list MUST be sorted to give correct answer • will see two different implementations of the algorithm 6.00.01X LECTURE 3 LINEAR SEARCH ON UNSORTED LIST def linear_search(L, e): found = False for i in range(len(L)): if e == L[i]: found = True return found . must look through all elements to decide it’s not there . O(len(L)) for the loop * O(1) to test if e == L[i] . overall complexity is O(n) – where n is len(L) 6.00.01X LECTURE 4 CONSTANT TIME LIST ACCESS . if list is all ints … ◦ ith element at ◦ base + 4*I .if list is heterogeneous ◦ indirection ◦ references to other objects … 6.00.01X LECTURE 5 6.00.01X LECTURE 6 LINEAR SEARCH ON SORTED LIST def search(L, e): for i in range(len(L)): if L[i] == e: return True if L[i] > e: return False return False . must only look until reach a number greater than e . O(len(L)) for the loop * O(1) to test if e == L[i] . overall complexity is O(n) – where n is len(L) 6.00.01X LECTURE 7 USE BISECTION SEARCH 1. -
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. -
3 Algorithms and Data Structures
3 Algorithms and Data Structures Program ®le for this chapter: algs What's wrong with this procedure? to process.sentence :sent output fput (process.word first :sent) (process.sentence bf :sent) end If you said ªIt's a recursive procedure without a stop rule,º you've solved a simple problem in analysis of algorithms. This branch of computer science is concerned with the correctness and the ef®ciency of programs. The ®eld is called analysis of algorithms rather than analysis of programs because the emphasis is on the meaning of a program (how you might express the program in English) and not on the details of its expression in a particular language. For example, the error in the procedure to process.sentence :sent if emptyp :sent [output []] output fput (process.word first :sent) (process.snetence bf :sent) end is just as fatal as the error in the ®rst example, but there isn't much of theoretical interest to say about a misspelled procedure name. On the other hand, another branch of computer science, program veri®cation, is concerned with developing techniques to ensure that a computer program really does correctly express the algorithm it is meant to express. The examples I've given so far are atypical, it's worth noting, in that you were able to see the errors in the procedures without having any real idea of what they do! Without seeing process.word you can tell that this program is doing something or other to each word of a sentence, but you don't know whether the words are being translated 107 to another language, converted from upper case to lower case letters, translated into a string of phoneme codes to be sent to a speech synthesizer, or what. -
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. -
4Th, the Friendly Forth Compiler
4tH, the friendly Forth compiler J.L. Bezemer July 14, 2021 Contents 1 What’s new 19 I Getting Started 24 2 Overview 25 2.1 Introduction . 25 2.2 History . 25 2.3 Applications . 26 2.4 Architecture . 26 2.4.1 The 4tH language . 28 2.4.2 H-code . 28 2.4.3 H-code compiler . 29 2.4.4 Error handling . 30 2.4.5 Interfacing with C . 30 3 Installation Guide 32 3.1 About this package . 32 3.1.1 Example code . 32 3.1.2 Main program . 32 3.1.3 Unix package . 33 3.1.4 Linux package . 34 3.1.5 Android package . 38 3.1.6 MS-DOS package . 40 3.1.7 MS-Windows package . 41 3.2 Setting up your working directory . 43 3.3 Now what? . 43 3.4 Pedigree . 43 3.5 Contributors . 44 1 CONTENTS 2 3.6 Questions . 44 3.6.1 4tH website . 44 3.6.2 4tH Google group . 45 3.6.3 Newsgroup . 45 4 A guided tour 46 4.1 4tH interactive . 46 4.2 Starting up 4tH . 46 4.3 Running a program . 47 4.4 Starting an editing session . 47 4.5 Writing your first 4tH program . 48 4.6 A more complex program . 52 4.7 Advanced features . 56 4.8 Suspending a program . 63 4.9 Calculator mode . 65 4.10 Epilogue . 65 5 Frequently asked questions 66 II Primer 69 6 Introduction 70 7 4tH fundamentals 71 7.1 Making calculations without parentheses . 71 7.2 Manipulating the stack . -
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. -
COMPUTERSCIENCE Science
BIBLIOGRAPHY DEPARTMENT OF COMPUTER SCIENCE TECHNICAL REPORTS, 1963- 1988 Talecn Marashian Nazarian Department ofComputer Science Stanford University Stanford, California 94305 1 X Abstract: This report lists, in chronological order, all reports published by the Stanford Computer Science Department (CSD) since 1963. Each report is identified by CSD number, author's name, title, number of pages, and date. If a given report is available from the department at the time of this Bibliography's printing, price is also listed. For convenience, an author index is included in the back of the text. Some reports are noted with a National Technical Information Service (NTIS) retrieval number (i.e., AD-XXXXXX), if available from the NTIS. Other reports are noted with Knowledge Systems Laboratory {KSL) or Computer Systems Laboratory (CSL) numbers (KSL-XX-XX; CSL-TR-XX-XX), and may be requested from KSL or (CSL), respectively. 2 INSTRUCTIONS In the Bibliography which follows, there is a listing for each Computer Science Department report published as of the date of this writing. Each listing contains the following information: " Report number(s) " Author(s) " Tide " Number ofpages " Month and yearpublished " NTIS number, ifknown " Price ofhardcopy version (standard price for microfiche: $2/copy) " Availability code AVAILABILITY CODES i. + hardcopy and microfiche 2. M microfiche only 3. H hardcopy only 4. * out-of-print All Computer Science Reports, if in stock, may be requested from following address: Publications Computer Science Department Stanford University Stanford, CA 94305 phone: (415) 723-4776 * 4 % > 3 ALTERNATIVE SOURCES Rising costs and restrictions on the use of research funds for printing reports have made it necessary to charge for all manuscripts. -
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. -
Biography Five Related and Significant Publications
GUY BLELLOCH Professor Computer Science Department Carnegie Mellon University Pittsburgh, PA 15213 [email protected], http://www.cs.cmu.edu/~guyb Biography Guy E. Blelloch received his B.S. and B.A. from Swarthmore College in 1983, and his M.S. and PhD from MIT in 1986, and 1988, respectively. Since then he has been on the faculty at Carnegie Mellon University, where he is now an Associate Professor. During the academic year 1997-1998 he was a visiting professor at U.C. Berkeley. He held the Finmeccanica Faculty Chair from 1991–1995 and received an NSF Young Investigator Award in 1992. He has been program chair for the ACM Symposium on Parallel Algorithms and Architectures, program co-chair for the IEEE International Parallel Processing Symposium, is on the editorial board of JACM, and has served on a dozen or so program committees. His research interests are in parallel programming languages and parallel algorithms, and in the interaction of the two. He has developed the NESL programming language under an ARPA contract and an NSF NYI award. His work on parallel algorithms includes work on sorting, computational geometry, and several pointer-based algorithms, including algorithms for list-ranking, set-operations, and graph connectivity. Five Related and Significant Publications 1. Guy Blelloch, Jonathan Hardwick, Gary L. Miller, and Dafna Talmor. Design and Implementation of a Practical Parallel Delaunay Algorithm. Algorithmica, 24(3/4), pp. 243–269, 1999. 2. Guy Blelloch, Phil Gibbons and Yossi Matias. Efficient Scheduling for Languages with Fine-Grained Parallelism. Journal of the ACM, 46(2), pp.