Algorithms

Winter Quarter 2016

Instructor: Yury Makarychev
TAs: Mrinalkanti Ghosh and Hing Yin Tsang

Course: TTIC 31010 and CMSC 37000-1
Lectures: Tuesday & Thursdays, 9:00-10:20, Stuart Hall, room 104 (STU 104)
Mailing list: algorithms-class-2015@ttic.edu . To subscribe to the course mailing list, send an email to algorithms-class-2016+subscribe@ttic.edu (with any subject and body). You should get a confirmation email in about 5 minutes, reply to this email or click on a link inside. If you cannot subscribe to the mailing list, please contact me.
Textbook: Algorithm Design by Kleinberg and Tardos.

Office hours:

Yury: Tuesdays, 10:45–11:45am at TTIC 437, or by appointment
Mrinalkanti: Fridays, 3:00–4:00pm at TTIC 405
Hing Yin: Mondays, 3:00–4:00pm at Young 208A

Requirements: There will be 3 homework assignments, 3 short in-class quizzes, a midterm and final exam.
Grading: homeworks 45%, quizzes 5%, midterm 20%, final 30%

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

Assignment #1 (due on February 2)
Assignment #2 (due on February 16)
Assignment #3 (due on March 8)

Tentative Schedule

January 5: Greedy Algorithms (Chapter 4)
greedy algorithms, activity selection problem, minimum weighted completion time
January 7: Greedy Algorithms, Huffman coding
minimum cost spanning trees, Prim's algorithm, Huffman coding
January 12: Huffman coding
Huffman coding, a greedy algorithm for Max Cut
January 14: Dynamic Programming (Chapter 6)
Weighted Interval Scheduling, Typesetting problem
January 19: Quiz #1, Dynamic Programming
Typesetting Problem, Knapsack problem
January 21: Dynamic Programming
Minimum Tree Bisection, the Longest Common Subsequence Problem
January 26: Dynamic Programming
the Bellman-Ford algorithm
January 28: Maximum Flow and Minimum Cut
definitions, the Ford—Fulkerson algorithm
February 2: Quiz #2, Max Flow and Min Cut, Maximum Matching
the Ford—Fulkerson algorithm (continued), matchings, Hall's theorem
February 4: Applications of Max Flow and Min Cut
matchings, multi–source/multi–sink single–commodity flow, edge disjoint paths, Menger's theorem, and other examples
February 9: Linear Programming (LP)
linear programming, feasible solution, optimal solution, bounded/unbounded linear programs, feasible polytope, vertices, canonical (standard) form, LP duality
February 11: LP Duality
the dual LP, the dual of the dual, weak duality, strong duality
February 16: Midterm Exam
February 23: LP Duality. Polynomial-time reductions.
the LP for Max Flow, its dual, polynomial-time reductions
February 25: Polynomial-time reductions. Classes P and NP.
March 1: NP, NP complete, and NP hard problems. Approximation algorithms.
March 3: Approximation algoritms.