CSE 548-01 (#84542), AMS 542-01 (#84639): Analysis of Algorithms, Fall 2017

Lecture Time and Location. MW 7:00 pm - 8:20 pm, Javits Lecture Hall 102, West Campus

Instructor. Rezaul A. Chowdhury (rezaul{at}cs{dot}stonybrook{dot}edu)
Office Hours. MW 5:00 pm - 6:30 pm, room 239 (New Computer Science Building)

Teaching Assistants.

Course Description. We will explore techniques for designing and analysing efficient algorithms, including recurrence relations and divide-and-conquer algorithms, dynamic programming, graph algorithms (e.g., network flow), amortized analysis, cache-efficient and external-memory algorithms, high probability bounds and randomized algorithms, parallel algorithms and multithreaded computations, NP-completeness and approximation algorithms, the alpha technique, and FFT ( Fast Fourier Transforms ).

Prerequisites. Some background in algorithms analysis (e.g., CSE 373) and programming languages (e.g., C/C++) is required (or consent of instructor).

Textbooks. Only the first one is required.

  1. Thomas Cormen, Charles Leiserson, Ronald Rivest, and Clifford Stein. Introduction to Algorithms (3rd Edition), MIT Press, 2009.
  2. Sanjoy Dasgupta, Christos Papadimitriou, and Umesh Vazirani. Algorithms (1st Edition), McGraw-Hill, 2006.
  3. Jon Kleinberg and Éva Tardos. Algorithm Design (1st Edition), Addison Wesley, 2005.
  4. Rajeev Motwani and Prabhakar Raghavan. Randomized Algorithms (1st Edition), Cambridge University Press, 1995.
  5. Vijay Vazirani. Approximation Algorithms, Springer, 2010.
  6. Joseph JáJá. An Introduction to Parallel Algorithms (1st Edition), Addison Wesley, 1992.

Course Requirements. There will be 4 homework assignments (mainly theory problems, but may include some programming assignments, too) and two in-class exams (one midterm and one toward the end; 75 minutes each). Each student will be responsible for scribing one lecture. The course grade will be based on the following.

Download the Latex template for scribe notes.

Blackboard. Some course documents (e.g., scribe notes, homework solutions, etc.) will be available through Blackboard.

Students with Disabilities. Please check the DSS website for assistance.

Lecture Schedule.

Date Topic Notes / Reading Material
Mon, Aug 28 Introduction
  • Chapter 3 (Growth of Functions), Introduction to Algorithms (3rd Edition) by Cormen et al.
Wed, Aug 30 Introduction (continued) -
Mon, Sep 4 No Class
(Labor Day)
-
Wed, Sep 6 Introduction (continued)

Integer Multiplication & Karatsuba's Algorithm

Matrix Multiplication & Strassen's Algorithm
  • Chapter 2 (Divide-and-Conquer Algorithms), Section 2.1 (Multiplication), Algorithms (1st Edition) by Dasgupta et al.
  • [optional] Anatolii A. Karatsuba, “The Complexity of Computations”, Proceedings of the Steklov Institute of Mathematics, 211:169-183, 1995.
Mon, Sep 11 Matrix Multiplication & Strassen's Algorithm (continued)

Polynomial Multiplication & the Fast Fourier Transform
  • Chapter 4 (Divide-and-Conquer), Section 4.2 (Strassen’s Algorithm for Matrix Multiplication), Introduction to Algorithms (3rd Edition) by Cormen et al.
  • [optional] Chapter 9 (Algebraic and Numeric Algorithms), Section 9.5.2 (Strassen’s Algorithm), Introduction to Algorithms - A Creative Approach (1st Edition) by Udi Manber.
  • Volker Strassen, “Gaussian Elimination is not Optimal”, Numerische Mathematik, 13:354-356, 1969.
Wed, Sep 13 Polynomial Multiplication & the Fast Fourier Transform (continued)

Additional Slides
  • Chapter 2 (Divide-and-Conquer Algorithms), Section 2.6 (The Fast Fourier Transform), Algorithms (1st Edition) by Dasgupta et al.
  • Chapter 30 (Polynomials and the FFT), Introduction to Algorithms (3rd Edition) by Cormen et al.
Mon, Sep 18 Polynomial Multiplication & the Fast Fourier Transform (continued)
Wed, Sep 20 The Master Theorem

Akra-Bazzi Recurrences
  • Chapter 4 (Divide-and-Conquer), Section 4.5 (The Master Method for Solving Recurrences) and Section 4.6 (Proof of the Master Method), Introduction to Algorithms (3rd Edition) by Cormen et al.
Mon, Sep 25 Akra-Bazzi Recurrences
  • Chapter 9 (Medians and Order Statistics), Section 9.3 (Selection in Worst-case Linear Time), Introduction to Algorithms (3rd Edition) by Cormen et al.
  • Mohamad Akra and Louay Bazzi, “On the Solution of Linear Recurrence Equations”, Computational Optimization and Applications, 10(2):195–210, 1998.
Wed, Sep 27 Akra-Bazzi Recurrences (continued)
Mon, Oct 2 Akra-Bazzi Recurrences (continued)
Linear Recurrences with Constant Coefficients (self-study)
Generating Functions
  • Tom Leighton, “Notes on Better Master Theorems for Divide-and-Conquer Recurrences”, 1996.
  • [optional] Chapter 7 (Advanced Counting Techniques), Section 7.2 (Solving Linear Recurrence Relations), Discrete Mathematics and its Applications (6th Edition) by Kenneth Rosen.
  • [optional] Chapter 7 (Generating Functions), Concrete Mathematics (2nd Edition) by Ronald Graham, Donald Knuth, and Oren Patashnik.
Wed, Oct 4 Class Canceled -
Mon, Oct 9 Generating Functions (continued)
  • [optional] Chapter 10 (Ordinary Generating Functions), Section 10.3 (Manipulating Generating Functions), Example 10.12 (The Average Time for Quicksort), Foundations of Combinatorics with Applications by Edward A. Bender and S. Gill Williamson.
Wed, Oct 11 Exam 1 -
Mon, Oct 16 Generating Functions (continued)
Amortized Analysis
  • Chapter 17 (Amortized Analysis), Introduction to Algorithms (3rd Edition) by Cormen et al.
Wed, Oct 18 Amortized Analysis (continued)
Binomial Heaps
Mon, Oct 23 Binomial Heaps (continued)
  • [optional] Chapter 8 (Binomial Heaps), The Design and Analysis of Algorithms (1992) by Dexter Kozen.
Wed, Oct 25 Binomial Heaps (continued)
  • [optional] Chapter 19 (Binomial Heaps), Introduction to Algorithms (2nd Edition) by Cormen et al.
Mon, Oct 30 Dijkstra's SSSP & Fibonacci Heaps
  • Chapter 19 (Fibonacci Heaps), Introduction to Algorithms (3rd Edition) by Cormen et al.
Wed, Nov 1 Dijkstra's SSSP & Fibonacci Heaps (continued)
High Probability Bounds and Randomized Algorithms
Fri, Nov 3 High Probability Bounds and Randomized Algorithms (continued)
  • [optional] Chapter 6 (Algorithms Involving Sequences and Sets), Section 6.9.2 (A Coloring Problem), Introduction to Algorithms - A Creative Approach (1st Edition) by Udi Manber.
Mon, Nov 6 High Probability Bounds and Randomized Algorithms (continued)
  • [optional] Chapter 1 (Introduction), Section 1.1 (A Min-Cut Algorithm), Randomized Algorithms (1st Edition) by Rajeev Motwani and Prabhakar Raghavan.
Fri, Nov 10 High Probability Bounds and Randomized Algorithms (continued)
Mon, Nov 13 High Probability Bounds and Randomized Algorithms (continued)
  • Chapter 7 (Quicksort), Section 7.4 (Analysis of Quicksort), Introduction to Algorithms (3rd Edition) by Cormen et al.
Wed, Nov 15 High Probability Bounds and Randomized Algorithms (continued)
Analyzing Parallel Algorithms
Mon, Nov 20 - -
Wed, Nov 22 No Class
(Thanksgiving Break)
-
Mon, Nov 27 - -
Wed, Nov 29 Exam 2 -
Mon, Dec 4 - -
Wed, Dec 6 - -

Homeworks.

Old Homeworks.

Exams.

Old Exams.

Additional Resources in SBUCS.