1. COMPSCI 330 Design and Analysis of Algorithms
Rong Ge

2. Algorithms
From wiki: In mathematics and computer science, an algorithm is a self-contained sequence of actions to be performed.

3. Designing an Algorithm - Basics
Divide and conquer
Dynamic programming
Greedy algorithms

4. Designing an Algorithm - Examples
Graph algorithms
Shortest paths
Minimum spanning tree
Bipartite matching
Data structrues
Hashing
Disjoint sets

5. Designing Algorithm – General Tools
Linear Programming
Formulation
Duality
Algorithms

6. Designing Algorithm - Intractability
What (we believe) cannot have efficient algorithms.
P vs. NP
NP completeness
Reductions

7. Final Format 5 problems Problem 1 Warm-up
Possible topics: recursions/running graph algorithms/graph examples
Problems 2-4 Topics covered in previous midterms
Basic design techniques
Graph algorithms
Linear Programming
There might be probabilities in the problems.
Problem 5 Reduction
You will be given an NP-hard problem as starting point (make sure to reduce this problem to the new problem)

8. Example of “probabilities in problems”
You are trying to predict the result of election based on available data. There are n states, state i has vi votes, and there are m votes in total. Based on the current data, state i has probability pi to vote for democratic party, and probability 1-pi to vote for republican party. Compute the exact probability of democratic party to win the election.