Spring 2016

Network flows is an exciting field that brings together what many students, practitioners, and researchers like best about the mathematical and computational sciences. It couples deep intellectual content with a remarkable range of applicability, covering literally thousands of applications in such wide-ranging fields as chemistry and physics, computer networking, most branches of engineering, manufacturing, public policy and social systems, scheduling and routing, telecommunications, and transportation. It is classical, dating from the work of Gustav Kirchhoff, and other eminent physical scientists of the last century, and yet vibrant and current, bursting with new results and new approaches.

This class will cover algorithms for network flow and related problems. We will cover both classical results and modern state-of-the-art algorithms for a number of network flow problems including the shortest paths, maximum flow, minimum cut, minimum cost flow, matching and multicommodity flow problems. The focus will be on learning about a number of different algorithmic techniques that have proved fruitful in this, and other areas. We will also discuss applications and related problems.

- Errata for the textbook
- Basics of Algorithm Analysis
- Running times of various functions
- Basic Graph Search
- Linear Time Minimum Spanning Trees
- Minimum Spanning Tree Mathematical Programs
- Shortest Paths
- Slides from a talk on implementing shortest path algorithms
- Johnson's Algorithm for All Pairs Shortest Paths
- Minimum Mean Cycle
- Maximum Flows
- paper on soviet rail system
- More Maximum Flows
- Applications of Max Flows
- Flow Decomposition
- Minimum Cost Flows
- Minimum Cost Flow via Capacity Scaling
- Matchings
- Non-bipartite matching
- Assignment Algorithm
- Min Cut paper
- Min Cut Algorithms
- Multicommmodity Flow
- Integral Multicommodity Flow paper
- Multiplicative Weights Algorithm
- Survey on Multiplicative Weights
- Approximation Algorithms 1 Background reading is CLRS chapter on Approximation Algorithms.
- Max Cut paper