Topics for the Final
CS 343: Analysis of Algorithms, Spring 2008

Please review class notes and the sections from chapters 1-8 that were covered in class. Review written and programming homework.

Topics on the final will include material covered on the midterm as well as the topics listed below.

Chapter 5: Divide and Conquer

• Methods for evaluating complexity of recursive algorithms:
  • Unrolling/Telescoping.
  • Master Theorem (long and short versions)
• Applications: mergesort, stoogesort, binary search, closest pair, hidden surface removal

Chapter 6: Dynamic Programming

• What is DP? When is it used? What is the "procedure" for finding solutions?
• What is memoization?
• Applications: weighted interval scheduling, Chapest path, 0-1 Knapsack, Pretty printing, LCS, segmented least squares, Bellman-Ford Shortest Path Algorithm (negative costs), ordered graph, Zion

Chapter 7: Network Flow (Sections 1-3)

• What is network flow?
• Maximum-Flow Problem: Ford Fulkerson Algorithm - augmenting paths in a residual graph

Chapter 8: NP and Intractability (Sections 1-4)

• Complexity Comparison: P, NP, NP-Complete, NP-Hard, EXP
• Know Definitions: decision problems, NP, NP-complete, NP hard, polynomial reducibility, polynomial transforms, certificate & certifiers
• Examples of NP/NP-Complete problems: Independent Set, Vertex Cover, Circuit Satisfiability, 3-Satisfiability. TSP, Hamiltonian Cycle, etc
• Significance and meaning of P=NP.