Course Outline

Introduction to Analysis of Algorithms
1. Overview of algorithms
2. Analyzing algorithms
3. Designing algorithms
4. Proofs
Growth of Functions and Notations
1. Big Oh, Little Oh, Big Omega, Little Omega, and Big Theta notations
2. NP-Complete Problems
3. Approximation Algorithms
Recurrences
1. Iteration method
2. Recursion-tree method
3. Master method
Sorting in Linear Time
1. Lower bounds for sorting
2. Counting sort
3. Radix sort
Medians and Order Statistics
1. Minimum and maximum
2. Selection in expected linear time
3. Selection in worst-case linear time
Greedy Algorithms
1. Elements of the greedy strategy
2. Huffman codes
Elementary Graph Algorithms
1. Representations of graphs
2. Breadth-first search
3. Depth-first search
4. Topological search
5. Strongly connected components
Minimum Spanning Trees
1. Algorithms of Kruskal and Prim
Single-Source Shortest Path
1. Bellman-Ford algorithm
2. Single-source shortest paths in directed acyclic graphs
3. Dijkstra's algorithm
All-Pairs Shortest Paths
Maximum Flow
Distributed Algorithms
1. Distributed Paradigm
2. Consensus and Election

Revised 2012