| Date | Topic | Reading | |
| Session 1 | Introduction Network Flow Examples Linear Programming |
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| Session 2 | Linear Programming Continued LP Solutions: the Graphical Method LP Solutions: the Brute Force Method |
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| Session 3 | Assumptions of the LP Model Introduction to AMPL | ||
| Session 4 |
Introduction to Network Flows |
Ahuja, Magnanti, and Orlin (AMO): Chapter 1 | |
| Session 5 |
Introduction to Network Flows Continued |
AMO: Chapter 1 | |
| Session 6 | Algorithm Design and Analysis | AMO: Pages 41 and 42
AMO: Chapters 2.3, 3.1, and 3.2 (through page 63) |
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| Session 7 | Search Algorithms | AMO: Chapter: 3.4 | |
| Session 8 | Search Algorithms Continued | AMO: Chapter: 3.4 | |
| Algorithms for the Shortest Path Problem: Introduction
Shortest Path Trees |
AMO Chapters: 4.1, 4.2, 4.3, and 4.4 | ||
| Session 9 | Shortest Path Applications | ||
| Dijkstra's Algorithm | AMO Chapter: 4.5 | ||
| Session 10 |
Dijkstra's Algorithm Continued The Bellman-Ford Algorithm |
AMO: Chapter 5.4 | |
| Session 11 | MCNFP and NegativeCycles | ||
| The Floyd-Warshall Algorithm | AMO: Chapter 5 | ||
| Session 12 | Overview of Shortest Path Algorithms | ||
| Session 13 | In-Class Exam 1 | ||
| Session 14 | Algorithms in AMPL | ||
| Session 15 | The Maximum Flow Problem | AMO: Chapter 6.1, 6.2, 6.3, and 6.4 | |
| Flows and Cuts | |||
| The Max-Flow Min-Cut Theorem | |||
| Session 16 | The Augmenting Path Algorithm | ||
| The Ford-Fulkerson Algorithm | AMO: Section 6.5 | ||
| Flows on Cycles | |||
| Max Flow with Non-Zero Lower Bounds | |||
| Session 17 | Max-Flow and Min-Cut Applications | AMO Section 8.1 | |
| Edge Connectivity
Vertex Connectivity |
Edge
Connectivity Applet
All-Pairs Minimum Cut | ||
| Session 18 | Even Max-Flow and Min-Cut Applications Playoff Races Scheduling on Parallel Machines and Distributed Computing | Baseball Elimination | |
| Session 19 | Max-Flow Min-Cut Applications Distributed Computing The Minimum Chain Covering Problem |
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| Matchings, Coverings, and Independent Sets | |||
| Maximum Weight Closure | Mining for Gold | ||
| Session 20 | In-Class Exam 2 | ||
| Session 21 | Review of the Simplex Method
LP in Two Dimensions LP's in Standard Form Basic Solutions Preview of the Simplex Method | AMO Appendix C | |
| Session 22 |
The Ratio Test Cramer's Rule |
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| Session 23 |
Introduction to the Network Simplex algorithm
Spanning Trees and Basic Feasible Solutions Node Potentials, and Reduced Arc Costs | AMO Chapter 11 | |
| Session 24 | Network Models with Integer Variables and/or Side Constraints | Warehouse Location Problem | |
| Session 25 | Maximum Concurrent Flow | ||
| Session 26 | Multicommodity Flows | ||
| Session 27 | Generalized Network Flows | ||
| Session 28 | Capstone Application: Survivable Network Design | Basic Mathematical Programming Models for Capacity Allocation in Mesh-Based Survivable Networks | |
| Session 29 | Review for Final |