CMPSCI 611: Graduate Theory of Algorithms

David Mix Barrington

Fall, 2005

This is a quick preliminary syllabus for CMPSCI 611. Chapter references are to the course text, which is lecture notes by Prof. Micah Adler, available at Collective Copies in Amherst starting 7 September 2005:

• Lectures 1-3: Prelinaries, Divide and Conquer
  • 8 Sept: Preliminaries, Mergesort, Master Theorem (1, 2.1)
  • 13 Sept: Strassen's Matrix Multiplication Algorithm, Closest Pairs (2.2-2.4)
  • 15 Sept: The Fast Fourier Transform (2.5)
• Lectures 4-7: Greedy Algorithms and Matroids
  • 20 Sept: Minimum Spanning Trees, Greedy Algorithms on Subset Systems (3.1, 3.2)
  • 22 Sept: Matroids (3.3)
  • 27 Sept: Bipartite Matchings (3.4)
  • 29 Sept: NO LECTURE (Dave away)
  • 4 Oct: The Union-Find Problem, Kruskal's Algorithm (3.5)
• Lectures 8-11: Dynamic Programming, Shortest Paths, and Network Flow
  • 6 Oct: The Knapsack Problem, Dynamic Programming, Floyd-Warshall (4.1-4.3)
  • 11 Oct: The Dijkstra and Seidel Algorithms (4.4, 4.5)
  • 13 Oct: More Seidel, Network Flow (4.6, 5.1)
  • 18 Oct: Network Flow, Ford-Fulkerson Algorithm (5.2-5.5)
• Lectures 12-15: Randomized Algorithms
  • 20 Oct: Quicksort, The Min-Cut Problem (6.1,6.2)
  • 25 Oct: Karger's Algorithm, Polynomial Identities, Matchings (6.3)
  • 26 Oct: MIDTERM EXAM on Lectures 1-11 (Chapters 1-5), 6:30-9:00 p.m., Herter 231.
  • 27 Oct: Primality Testing (6.4)
  • 1 Nov: Median Finding (6.5)
• Lectures 16-22: NP-Completeness and Approximation Algorithms
  • 3 Nov: NP-Completeness Fundamentals (7.1)
  • 8 Nov: NP-Completeness Examples (7.2)
  • 10 Nov: Subset Sum, Max-Cut (7.3)
  • 15 Nov: P versus NP, Approximations, Independent Set Problem (7.4, 8.1, 8.2)
  • 17 Nov: NO LECTURE (Dave away)
  • 22 Nov: More Approximations, Metric TSP Problem (8.3,8.4)
  • 29 Nov: Set Cover Problem, Poly-Time Approximation Schemes (8.5,8.6)
  • 1 Dec: NP-Hardness of Approximation Problems (8.7)
• Lectures 23-25: Linear Programming Linear Programming (Chapter 9)
  • 6 Dec: Linear Programming, Simplex Method (9.1,9.2)
  • 8 Dec: Analysis of the Simplex Method (9.3)
  • 13 Dec: Duality (9.4)

Last modified 7 September 2005