CSE 548-01 (#84542), AMS 542-01 (#84639): Analysis of Algorithms, Fall 2015

CSE 548-01 (#84542), AMS 542-01 (#84639): Analysis of Algorithms, Fall 2015

Lecture Time and Location. MoFr 1:00 pm - 2:20 pm, Earth & Space Sciences Building (069), West Campus

Instructor. Rezaul A. Chowdhury (rezaul{at}cs{dot}stonybrook{dot}edu)
Office Hours. Mo 11:00 am - 12:30 pm, Fr 3:00 pm - 4:30 pm, Room 239 (New Computer Science Building)

Grader. Srikant Aggarwal (sraggarwal{at}cs{dot}stonybrook{dot}edu)

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.

Thomas Cormen, Charles Leiserson, Ronald Rivest, and Clifford Stein. Introduction to Algorithms (3rd Edition), MIT Press, 2009.
Sanjoy Dasgupta, Christos Papadimitriou, and Umesh Vazirani. Algorithms (1st Edition), McGraw-Hill, 2006.
Jon Kleinberg and Éva Tardos. Algorithm Design (1st Edition), Addison Wesley, 2005.
Rajeev Motwani and Prabhakar Raghavan. Randomized Algorithms (1st Edition), Cambridge University Press, 1995.
Vijay Vazirani. Approximation Algorithms, Springer, 2010.
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 at the end; 75 minutes each). Each student will be responsible for scribing one lecture. The course grade will be based on the following.

Homeworks: 40% (the highest score will be worth 15%, the lowest score will be worth 5%, and the remaining two will be worth 10% each)
Exams: 45% (the higher of the two scores will be worth 30%, and the lower one 15%)
Scribe notes: 10%
Class paricipation and attendance: 5%

Download the Latex template for scribe notes.

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

Lecture Schedule.

Date	Topic	Notes / Reading Material
Mon, Aug 24	Introduction	Chapter 3 (Growth of Functions), Introduction to Algorithms (3rd Edition) by Cormen et al.
Fri, Aug 28	Introduction (continued) Integer Multiplication & Karatsuba's Algorithm	Chapter 2 (Divide-and-Conquer Algorithms), Section 2.1 (Multiplication), Algorithms (1st Edition) by Dasgupta et al.
Mon, Aug 31	Integer Multiplication & Karatsuba's Algorithm (continued) Matrix Multiplication & Strassen's Algorithm	[optional] Anatolii A. Karatsuba, “The Complexity of Computations”, Proceedings of the Steklov Institute of Mathematics, 211:169-183, 1995. 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.
Fri, Sep 4	Polynomial Multiplication & the Fast Fourier Transform	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 7	No Class (Labor Day)	-
Fri, Sep 11	Polynomial Multiplication & the Fast Fourier Transform (continued)	James W. Cooley and John W. Tukey, “An Algorithm for the Machine Calculation of Complex Fourier Series”, Mathematics of Computation, 19(90):297–301, 1965. [fun] Thomas S. Huang, “How the Fast Fourier Transform Got its Name”, Computer, 4(3), page 15, 1971.
Mon, Sep 14	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. Chapter 9 (Medians and Order Statistics), Section 9.3 (Selection in Worst-case Linear Time), Introduction to Algorithms (3rd Edition) by Cormen et al.
Fri, Sep 18	Akra-Bazzi Recurrences (continued)	Mohamad Akra and Louay Bazzi, “On the Solution of Linear Recurrence Equations”, Computational Optimization and Applications, 10(2):195–210, 1998.
Mon, Sep 21	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.
Fri, Sep 25	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.
Mon, Sep 28	Amortized Analysis	Chapter 17 (Amortized Analysis), Introduction to Algorithms (3rd Edition) by Cormen et al.
Fri, Oct 2	Amortized Analysis (continued) Binomial Heaps	Chapter 6 (Heapsort), Introduction to Algorithms (3rd Edition) by Cormen et al. Jean Vuillemin, “A data structure for manipulating priority queues”, Communications of the ACM, 21(4):309-315, 1978.
Mon, Oct 5	Binomial Heaps (continued)	[optional] Chapter 8 (Binomial Heaps), The Design and Analysis of Algorithms (1992) by Dexter Kozen.
Fri, Oct 9	Binomial Heaps (continued)	[optional] Chapter 19 (Binomial Heaps), Introduction to Algorithms (2nd Edition) by Cormen et al.
Mon, Oct 12	In-class Exam 1 (Midterm)	-
Fri, Oct 16	Binomial Heaps (continued) Dijkstra's SSSP & Fibonacci Heaps	Chapter 19 (Fibonacci Heaps), Introduction to Algorithms (3rd Edition) by Cormen et al.
Mon, Oct 19	Dijkstra's SSSP & Fibonacci Heaps (continued)	Michael L. Fredman and Robert E. Tarjan, “Fibonacci heaps and their uses in improved network optimization algorithms”, Journal of the ACM, 34(3):596-615, 1987.
Fri, Oct 23	Dijkstra's SSSP & Fibonacci Heaps (continued) High Probability Bounds and Randomized Algorithms	[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, Oct 26	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, Oct 30	High Probability Bounds and Randomized Algorithms (continued)	Torben Hagerup and Christine Rüb, “A Guided Tour of Chernoff Bounds”, Information Processing Letters, 33(6), pp. 305-308, 1990.
Mon, Nov 2	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.
Fri, Nov 6	High Probability Bounds and Randomized Algorithms (continued)	William Pugh, “Skip lists: a probabilistic alternative to balanced trees”, Communications of the ACM, 33(6):668-676, 1990.
Mon, Nov 9	Approximation Algorithms	Chapter 35 (Approximation Algorithms), Introduction to Algorithms (3rd Edition) by Cormen et al. Chapter 35 (Approximation Algorithms), Section 35.1 (The Vertex-Cover Problem), Introduction to Algorithms (3rd Edition) by Cormen et al. Chapter 35 (Approximation Algorithms), Section 35.2 (The Traveling-Salesman Problem), Introduction to Algorithms (3rd Edition) by Cormen et al.
Fri, Nov 13	Approximation Algorithms (continued)	Chapter 35 (Approximation Algorithms), Section 35.2.1 (The Traveling-Salesman Problem with the Triangle Inequality), Introduction to Algorithms (3rd Edition) by Cormen et al. Chapter 35 (Approximation Algorithms), Section 35.2.1 (The General Traveling-Salesman Problem), Introduction to Algorithms (3rd Edition) by Cormen et al.
Mon, Nov 16	Approximation Algorithms (continued)	Chapter 35 (Approximation Algorithms), Section 35.3 (The Set-Covering Problem), Introduction to Algorithms (3rd Edition) by Cormen et al.
Fri, Nov 20	Approximation Algorithms (continued)	Chapter 35 (Approximation Algorithms), Section 35.5 (The Subset-Sum Problem), Introduction to Algorithms (3rd Edition) by Cormen et al.
Mon, Nov 23	Analyzing Parallel Algorithms	[optional] Gordon E. Moore, “Cramming more components onto integrated circuits”, Electronics, 38(8), pp. 114-117, April 19, 1965. Chapter 5 (Analytical Modeling of Parallel Programs), Introduction to Parallel Computing (2nd Edition) by Grama et al. Gene Amdahl, “Validity of the Single Processor Approach to Achieving Large Scale Computing Capabilities”, Reprinted from the proceedings of the Spring Joint Computer Conference, AIFPS vol 30, pp. 483-485, 1967. Chapter 27 (Multithreaded Algorithms), Introduction to Algorithms (3rd Edition) by Cormen et al.
Fri, Nov 26	No Class (Thanksgiving Break)	-
Mon, Nov 30	Analyzing I/O and Cache Performance	Alok Aggarwal and Jeffrey S. Vitter, “The input/output complexity of sorting and related problems”, Communications of the ACM, 31(9), pp. 1116-1127, 1988. Matteo Frigo, Charles E. Leiserson, Harald Prokop, and Sridhar Ramachandran, “Cache-Oblivious Algorithms”, Proceedings of the 40th Annual Symposium on Foundations of Computer Science (FOCS), pp. 285-298, 1999. Jeffrey S. Vitter, “Algorithms and Data Structures for External Memory”, Series on Foundations and Trends in Theoretical Computer Science, Now Publishers, Hanover, MA, 2008.
Fri, Dec 4	In-class Exam 2	-

Homeworks.

Old Homeworks.

Spring 2015: hw1, hw2, hw3, hw4.
Spring 2014: hw1, hw2, hw3, hw4.
Fall 2012: hw1, hw2, hw3, hw4.

Exams.

Old Exams.

Spring 2015: exam 1, exam 2.
Spring 2014: exam 1, exam 2.
Fall 2012: exam 1, exam 2.

Additional Resources in SBUCS.

Algorithms Reading Group Meetings (CSE642: Seminar in Algorithms): This reading group provides a meeting place for Stony Brook faculty, postdocs, and students interested in the analysis of algorithms. We meet every Friday from 11:00 am - 12:30 pm in room 220 of the new CS building, and pose and solve interesting research problems.
Stony Brook Puzzle Society (SBPS): SBPS holds informal sessions on puzzles every week. Participants discuss, solve, and learn puzzles in mathematics, algorithms, data structures, programming, and logic. Discussions include puzzles asked in job interviews. Please consider attending.