15.082J | Fall 2010 | Graduate

Network Optimization

Lecture Notes

Lecture notes are available for this class in two formats. We recommend you view the Microsoft® PowerPoint® (PPT) versions, if possible, because they include motion. The animations referred to in the lecture notes in yellow boxes can be found in the animations section of the course. Please note that slides for Ses #18 are unavailable.

1 Introduction to network models (PDF) (PPT)
2 Computational complexity and data structures (PDF) (PPT - 1.5MB)
3 Graph search algorithms (PDF) (PPT)
4 Transformations and flow decomposition (PDF) (PPT)
5 Shortest paths: label setting algorithms (PDF) (PPT - 1.1MB)
6 The radix heap algorithm (PDF) (PPT)
7 Shortest paths: label correcting algorithms (PDF) (PPT)
8 Algorithm analysis (PDF) (PPT)
9 Basic algorithms for the maximum flow problem (PDF) (PPT - 1.0MB)
10 Midterm 1 (Ses #1-8)    
11 Combinatorial applications of maximum flows (PDF) (PPT)
12 Preflow push algorithms (PDF) (PPT)
13 More on preflow push algorithms (PDF) (PPT - 1.2MB)
14 Minimum cost flow: basic algorithms (PDF) (PPT)
15 Minimum cost flow: polynomial time algorithms (PDF) (PPT)
16 Applications of network flows; Linear programming review (PDF) (PPT - 2.4MB)
17 The network simplex algorithm (PDF) (PPT - 1.1MB)
18 NP-completeness    
19 Midterm 2 (Ses #9-17)    
20 Lagrangian relaxation 1 (PDF) (PPT - 1.3MB)
21 Lagrangian relaxation 2 (PDF) (PPT - 1.0MB)
22 Multicommodity flows 1 (PDF) (PPT)
23 Multicommodity flows 2 (PDF) (PPT)
24 Presentations of class projects    
25 Presentations of class projects (cont.)