CSE 385-01 (#91193): Analysis of Algorithms: Honors, Fall 2019

CSE 385-01 (#91193): Analysis of Algorithms: Honors, Fall 2019

Lecture Time and Location. MW 5:30 pm - 6:50 pm (Recitation: W 4:00 pm - 4:53 pm), Room 2129, Old CS Building, West Campus

Instructor. Rezaul A. Chowdhury (rezaul{at}cs{dot}stonybrook{dot}edu)
Office Hours. Mon 4:00 pm - 5:00 pm, Fri 6:00 pm - 8:00 pm, NCS 239 (New Computer Science Building)

Course Description. Mathematical analysis of a variety of computer algorithms including searching, sorting, matrix multiplication, fast Fourier transform, and graph algorithms. Time and space complexity. Upper-bound, lower-bound, and average-case analysis. Randomization. Introduction to NP completeness. Some machine computation is required for the implementation and comparison of algorithms.

Prerequisites. CSE 260; AMS 210 or MAT 211; Computer Science Honors Program or Honors College or WISE.

Textbooks. Only the first one is required.

Thomas Cormen, Charles Leiserson, Ronald Rivest, and Clifford Stein. Introduction to Algorithms (3rd Edition), MIT Press, 2009.
Steven Skiena. The Algorithm Design Manual (2nd Edition), Springer, 2008.
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.

Course Requirements. There will be 5 homework problem sets, one in-class midterm exam, and one final exam. The course grade will be based on the following.

Homeworks: 25% (worth 5% each)
In-class midterm (Monday, Oct 21): 25%
Final exam (Monday, Dec 16): 50%

Course Objectives. The ABET objectives for the course are as follows.

Ability to perform worst-case asymptotic algorithms analysis.
Ability to define and use classical combinatorial algorithms for problems such as sorting, shortest paths and minimum spanning trees.
Understanding of algorithmic techniques such as divide-and-conquer and dynamic programming.
Understanding of computational intractability and NP completeness.

Blackboard. Course documents (e.g., lecture slides, homework assignments) will be available through Blackboard.

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

Lecture Schedule.

Date	Topic	Notes / Reading Material
Mon, Aug 26	Introduction	[optional] Algorithmic Puzzles by Anany Levitin and Maria Levitin, Oxford University Press, 2011.
Wed, Aug 28	Asymptotic Analysis of Algorithms	Chapter 3 (Growth of Functions), Introduction to Algorithms (3rd Edition) by Cormen et al.
Mon, Sep 2	No Class (Labor Day)	-
Wed, Sep 4	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. 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.
Mon, Sep 9	Correctness of Algorithms: Insertion Sort and Selection Sort	Chapter 2 (Getting Started), Section 2.1 (Insertion Sort), Introduction to Algorithms (3rd Edition) by Cormen et al. Chapter 2 (Getting Started), Section 2.2 (Analyzing Algorithms), Introduction to Algorithms (3rd Edition) by Cormen et al.
Wed, Sep 11	Correctness of Algorithms: Merge Sort Deterministic Quicksort and Average Case Analysis	Chapter 2 (Getting Started), Section 2.3 (Designing Algorithms), Introduction to Algorithms (3rd Edition) by Cormen et al. Chapter 7 (Quicksort), Section 7.1 (Description of Quicksort), Introduction to Algorithms (3rd Edition) by Cormen et al. Chapter 7 (Quicksort), Section 7.2 (Performance of Quicksort), Introduction to Algorithms (3rd Edition) by Cormen et al.
Mon, Sep 16	Deterministic Quicksort and Average Case Analysis (continued) 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.
Wed, Sep 18	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 23	The Master Theorem	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.
Wed, Sep 25	Akra-Bazzi Recurrences Linear Recurrences with Constant Coefficients (self-study) Generating Functions	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. 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.
Mon, Sep 30	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 2	Dynamic Programming	Chapter 15 (Dynamic Programming), Section 15.1 (Rod Cutting), Introduction to Algorithms (3rd Edition) by Cormen et al.
Mon, Oct 7	Dynamic Programming (continued)	Chapter 15 (Dynamic Programming), Section 15.2 (Matrix-chain Multiplication), Introduction to Algorithms (3rd Edition) by Cormen et al. Rezaul Chowdhury, Pramod Ganapathi, Steven Tschudi, Jesmin Jahan Tithi, Charles Bachmeier, Bradley C. Kuszmaul, Charles E. Leiserson, Armando Solar-Lezama, and Yuan Tang, “AutoGen: Automatic Discovery of Efficient Recursive Divide-&-Conquer Algorithms for Solving Dynamic Programming Problems”, ACM Transactions on Parallel Computing, 4(1):4, 2017.
Wed, Oct 9	Dynamic Programming (continued)	Chapter 15 (Dynamic Programming), Section 15.3 (Elements of Dynamic Programming), Introduction to Algorithms (3rd Edition) by Cormen et al. Chapter 15 (Dynamic Programming), Section 15.4 (Longest Common Subsequence), Introduction to Algorithms (3rd Edition) by Cormen et al. Chapter 15 (Dynamic Programming), Section 15.5 (Optimal Binary Search Trees), Introduction to Algorithms (3rd Edition) by Cormen et al. Rezaul Chowdhury and Vijaya Ramachandran, “Cache-oblivious Dynamic Programming”, Proceedings of the 17th annual ACM-SIAM symposium on Discrete algorithm, pp. 591-600, 2006.
Mon, Oct 14	No Class (Fall Break)	-
Wed, Oct 16	Heaps and Heapsort	Chapter 6 (Heapsort), Section 6.1 (Heaps), Introduction to Algorithms (3rd Edition) by Cormen et al. Chapter 6 (Heapsort), Section 6.2 (Maintaining the Heap Property), Introduction to Algorithms (3rd Edition) by Cormen et al. Chapter 6 (Heapsort), Section 6.3 (Bulding a Heap), Introduction to Algorithms (3rd Edition) by Cormen et al. Chapter 6 (Heapsort), Section 6.4 (The Heapsort Algorithm), Introduction to Algorithms (3rd Edition) by Cormen et al. Chapter 6 (Heapsort), Section 6.5 (Priority Queues), Introduction to Algorithms (3rd Edition) by Cormen et al.
Mon, Oct 21	Midterm	-
Wed, Oct 23	Greedy Algorithms	Chapter 16 (Greedy Algorithms), Section 16.1 (An Activity Selection Problem), Introduction to Algorithms (3rd Edition) by Cormen et al. Chapter 16 (Greedy Algorithms), Section 16.2 (Elements of the Greedy Strategy), Introduction to Algorithms (3rd Edition) by Cormen et al. Chapter 23 (Minimum Spanning Trees), Section 23.1 (Growing a Minimum Spanning Tree), Introduction to Algorithms (3rd Edition) by Cormen et al. Chapter 23 (Minimum Spanning Trees), Section 23.2 (The Algorithms of Kruskal and Prim), Introduction to Algorithms (3rd Edition) by Cormen et al.
Mon, Oct 28	Greedy Algorithms (continued)	Chapter 24 (Single-Source Shortest Paths), Section 24.3 (Dijkstra's Algorithm), Introduction to Algorithms (3rd Edition) by Cormen et al. Mo Chen, Rezaul Chowdhury, Vijaya Ramachandran, David Lan Roche, and Lingling Tong, “Priority Queues and Dijkstra's Algorithm”, UT Austin, Department of Computer Sciences, Technical Report TR-07-54, Oct. 2007.
Wed, Oct 30	Amortized Analysis Binomial Heaps	Chapter 17 (Amortized Analysis), 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, Nov 4	Binomial Heaps (continued)	[optional] Chapter 8 (Binomial Heaps), The Design and Analysis of Algorithms (1992) by Dexter Kozen.
Wed, Nov 6	Binomial Heaps (continued) Dijkstra's SSSP & Fibonacci Heaps	[optional] Chapter 19 (Binomial Heaps), Introduction to Algorithms (2nd Edition) by Cormen et al. Chapter 19 (Fibonacci Heaps), Introduction to Algorithms (3rd Edition) by Cormen et al.
Mon, Nov 11	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.
Wed, Nov 13	More Graph Algorithms: Basic and Beyond	Chapter 22 (Elementary Graph Algorithms), Section 22.2 (Breadth-first search), Introduction to Algorithms (3rd Edition) by Cormen et al. Chapter 22 (Elementary Graph Algorithms), Section 22.3 (Depth-first search), Introduction to Algorithms (3rd Edition) by Cormen et al. Chapter 22 (Elementary Graph Algorithms), Section 22.4 (Topological sort), Introduction to Algorithms (3rd Edition) by Cormen et al. Chapter 22 (Elementary Graph Algorithms), Section 22.5 (Strongly connected components), Introduction to Algorithms (3rd Edition) by Cormen et al. Chapter 24 (Single-Source Shortest Paths), Section 24.1 (The Bellman-Ford algorithm), Introduction to Algorithms (3rd Edition) by Cormen et al. Chapter 24 (Single-Source Shortest Paths), Section 24.2 (Single-source shortest paths in directed acyclic graphs), Introduction to Algorithms (3rd Edition) by Cormen et al.
Mon, Nov 18	Network Flow	Chapter 26 (Maximum Flow), Section 26.1 (Flow networks), Introduction to Algorithms (3rd Edition) by Cormen et al. Chapter 26 (Maximum Flow), Section 26.2 (The Ford-Fulkerson method), Introduction to Algorithms (3rd Edition) by Cormen et al.
Wed, Nov 20	Network Flow (continued) All-Pairs Shortest Paths	Chapter 26 (Maximum Flow), Section 26.3 (Maximum bipartite matching), Introduction to Algorithms (3rd Edition) by Cormen et al. Chapter 25 (All-Pairs Shortest Paths), Section 25.1 (Shortest paths and matrix multiplication), Introduction to Algorithms (3rd Edition) by Cormen et al. Chapter 25 (All-Pairs Shortest Paths), Section 25.2 (The Floyd-Warshall algorithm), Introduction to Algorithms (3rd Edition) by Cormen et al.
Mon, Nov 25	Backtracking	Chapter 2 (Backtracking), Algorithms (1st Edition) by Jeff Erickson
Wed, Nov 27	No Class (Thanksgiving Break)	-
Mon, Dec 2	Randomized Algorithms and High Probability Bounds	Appendix C (Counting and Probability), Introduction to Algorithms (3rd Edition) by Cormen et al. [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. [optional] Chapter 1 (Introduction), Section 1.1 (A Min-Cut Algorithm), Randomized Algorithms (1st Edition) by Rajeev Motwani and Prabhakar Raghavan. [optional] Torben Hagerup and Christine Rüb, “A Guided Tour of Chernoff Bounds”, Information Processing Letters, 33(6), pp. 305-308, 1990. [optional] Chapter 7 (Quicksort), Section 7.4 (Analysis of Quicksort), Introduction to Algorithms (3rd Edition) by Cormen et al. William Pugh, “Skip lists: a probabilistic alternative to balanced trees”, Communications of the ACM, 33(6):668-676, 1990.
Wed, Dec 4	NP-Completeness	Chapter 8 (NP-Complete Problems), Algorithms (1st Edition) by Dasgupta et al.
Mon, Dec 9	Analyzing Parallel Algorithms (Guest Lecturer: Zafar Ahmad)	[optional] Chapter 5 (Analytical Modeling of Parallel Programs), Introduction to Parallel Computing (2nd Edition) by Grama et al. Chapter 27 (Multithreaded Algorithms), Introduction to Algorithms (3rd Edition) by Cormen et al. [optional] Gordon E. Moore, “Cramming more components onto integrated circuits”, Electronics, 38(8), pp. 114-117, April 19, 1965. 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.
[Slides on BB]	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. 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 35.2.2 (The General Traveling-Salesman Problem), Introduction to Algorithms (3rd Edition) by Cormen et al. Chapter 35 (Approximation Algorithms), Section 35.3 (The Set-Covering Problem), Introduction to Algorithms (3rd Edition) by Cormen et al. Chapter 35 (Approximation Algorithms), Section 35.5 (The Subset-Sum Problem), Introduction to Algorithms (3rd Edition) by Cormen et al.
[Slides on BB]	The Inverse Ackermann Function, Union-Find, and Partial Sums	Chapter 21 (Data Structures for Disjoint Sets), Introduction to Algorithms (3rd Edition) by Cormen et al. Raimund Seidel and Micha Sharir, “Top-Down Analysis of Path Compression”, SIAM Journal on Computing, 34(3):515-525, 2005. [optional] Andrew C. Yao, “Space-Time Tradeoff for Answering Range Queries”, Proceedings of the 14th Annual ACM Symposium on Theory of Computing (STOC), pp. 128-136, 1982. [optional] Bernard Chazelle and Burton Rosenberg, “Computing Partial Sums in Multidimensional Arrays”, Proceedings of the 5th Annual Symposium on Computational Geometry (SCG), pp. 131-139, 1989.
[Slides on BB]	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.

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 Wednesday from 11:00 am - 12:30 pm in room 120 of the new CS building, and pose and solve interesting open research problems.