Topics for the Week of Feb 18, 2008
CS343: Analysis of Algorithms

Assignments:

• Work on programming problem - Dijkstra's algorithm and heaps.

Lecture: Continue discussion of chapter 4: Greedy Algorithms

• Interval scheduling
• Shortest path for weighted directed graph - Dijkstra's Algorithm
• Minimum Spanning Tree:
  • Kruskal's Algorithm and the Union-Find Data Structure
  • Prim's Algorithm
  • Reverse-Delete Algorithm
• Huffman Codes and Data Compression
• We will not cover sections 4.7 Clustering or 4.9 Minimum-Cost Arborescences.
• Examples of Algorithms
  • Dijkstra, Prim, Kruskal
  • Reverse-Delete
  • Union-Find:
    • Maze generation using Kruskal's algorithm with union-find.
    • Union-Find
    • Another union find.
    • Complexity of Union-find: O(n &alpha(n)) where &alpha(n) is the inverse Ackermann Function
  • BFS: wire routing
• Analyzing Greedy algorithms:
  • Determining the "Greedy Rule"
  • Staying ahead: Given an optimal solution O, show that the greedy solution "stays ahead" of O
  • The Exchange Argument