Algorithms

Winter Quarter 2018

Instructor: Yury Makarychev TAs: Haris Angelidakis and David Kim   Course: TTIC 31010 and CMSC 37000-1 Lectures: Tuesdays & Thursdays, 9:30am-10:50am, TTIC, room 526 Tutorials: Wednesdays, 3:30pm-4:20pm, TTIC, room 530 Canvas course site: canvas.uchicago.edu/courses/13223 Textbook: Algorithm Design by Kleinberg and Tardos   Office hours: Yury: Tuesdays, 10:55–11:55am at TTIC 437, or by appointment Haris Angelidakis: Thursdays, 11am–12pm at TTIC 405 David Kim: Wednesdays, 4:30pm–5:30pm at TTIC 435 (TTIC Library) Requirements: There will be 3 homework assignments, 2-3 short in-class quizzes, a midterm and final exam. Grading: homeworks 45%, quizzes 5%, midterm 20%, final 30%; extra credit for class participation Description: This is a graduate-level course on algorithms, with an emphasis on computational problems that are central to both theory and practice. The course focuses on developing techniques for the design and rigorous analysis of algorithms and data structures for such problems.

W. Kandinsky, Squares with Concentric Circles, 1913. A dynamic programming algorithm solves sub-problems of the original problem and stores solutions to the sub-problems in a table.

Homework Assignments

• Will be posted on the Canvas web site for the course.

Tentative Schedule

1. January 4: Greedy Algorithms (Chapter 4)
   greedy algorithms, interval scheduling problem, minimum weighted completion time
2. January 9: Greedy Algorithms, Huffman coding
   minimum cost spanning trees, Prim's algorithm, Huffman coding
3. January 11: Huffman coding
   Huffman coding, a greedy algorithm for Max Cut
4. January 16: Dynamic Programming (Chapter 6)
   weighted interval scheduling, typesetting problem
5. January 18: Quiz #1, Dynamic Programming
   typesetting problem, knapsack problem
6. January 23: Dynamic Programming
   minimum tree bisection, the longest common subsequence problem
7. January 25: Dynamic Programming
   the Bellman-Ford algorithm
8. January 30: Maximum Flow and Minimum Cut
   definitions, the Ford—Fulkerson algorithm
9. February 1: Max Flow and Min Cut, Maximum Matching
   the Ford—Fulkerson algorithm (continued), matchings, Hall's theorem
10. February 6: Quiz #2, Applications of Max Flow and Min Cut
    matchings, multi–source/multi–sink single–commodity flow, edge disjoint paths, Menger's theorem, and other examples
11. February 8: Linear Programming (LP)
    linear programming, feasible solution, optimal solution, bounded/unbounded linear programs, feasible polytope, vertices, canonical (standard) form, LP duality
12. February 13: LP Duality
    the dual LP, the dual of the dual, weak duality, strong duality
13. February 15: Midterm Exam
14. February 20: LP Duality. Polynomial-time reductions.
    the LP for Max Flow, its dual, polynomial-time reductions
15. February 22: Polynomial-time reductions. Classes P and NP.
16. February 27: NP, NP complete, and NP hard problems. Approximation algorithms.
17. March 1: Quiz 3, Approximation algorithms.
18. March 6: Randomized algorithms.