EMIS 8374
Spring 2006
Lecture Notes

Date	Topic	Reading
17 January Session 1	Introduction Network Flow Examples Linear Programming	Appendix A.1 in Glover, Klingman, and Phillips (GKP)
19 January Session 2	Linear Programming Continued LP Solutions: the Graphical Method LP Solutions: the Brute Force Method
24 January Session 3	Assumptions of the LP Model Introduction to AMPL
26 January Session 4	NSC example in AMPL Hypertext notes for NSC example AMPL Model and Data Files for the Diet Problem.
	Introduction to Network Flows: Slides 1 through 34	Ahuja, Magnanti, and Orlin (AMO): Chapter 1 GKP: Chapter 1
31 January Session 5	Introduction to Network Flows Continues	AMO: Chapter 1 GKP: Chapter 1
	MCNFP Formulation of NSC Problem Review of the MCNFP	AMPL Model for MCNFP
2 Februrary Session 6	Algorithm Design and Analysis	AMO: Pages 41 and 42 AMO: Chapters 2.3, 3.1, and 3.2 (through page 63)
7 February Session 7	Search Algorithms	AMO: Chapter: 3.4
9 February 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
14 February Session 9	Shortest Path Applications
	Dijkstra's Algorithm	AMO Chapter: 4.5
16 February Session 10	Dijkstra's Algorithm Continued. The Bellman-Ford Algorithm	AMO: Chapter 5.4
	MCNFP and NegativeCycles
21 February Session 11	The Floyd-Warshall Algorithm Example 1	AMO: Chapter 5
	Overview of Shortest Path Algorithms
	Sets in AMPL
23 February Session 12	Midterm 1
28 February Session 13	Algorithms in AMPL	AMPL code
	The Maximum Flow Problem	AMO: Chapter 6.1, 6.2, 6.3, and 6.4
	Flows and Cuts
	The Max-Flow Min-Cut Theorem
2 March Session 14	The Augmenting Path Algorithm
	The Ford-Fulkerson Algorithm	AMO: Section 6.5
	Flows on Cycles
	Max Flow with Non-Zero Lower Bounds
7 March Session 15	Max-Flow Min-Cut Applications	AMO Section 8.1
	Edge Connectivity Vertex Connectivity	Edge Connectivity Applet All-Pairs Minimum Cut
	Exam Solutions
9 March Session 16	Guest Lecturer: Anusha Madhavan	Open Shortest Paths First (OSPF)
21 March Session 17	Even More Max-Flow Min-Cut Applications Playoff Races Scheduling on Parallel Machines and Distributed Computing	Baseball Elimination
23 March Session 18	Even More Max-Flow Min-Cut Applications Distributed Computing Minimum Chain Covering Problem
28 March Session 19	Still More Max-Flow Min-Cut Applications Matchings, Coverings, and Independent Sets
	Maximum Weight Closure	AMO Chapter 19.2 Mining for Gold AMPL data file
30 March Session 19	Midterm 2	Lectures 6 through 11
4 April Session 21	Review of the Simplex Method LP in Two Dimensions LP's in Standard Form Basic Solutions Preview of the Simplex Method Simplex Method Example	AMO Appendix C GKP Appendix A
6 April Session 22	The Ratio Test Introduction to the Network Simplex Algorithm Node Potentials, and Reduced Arc Costs	AMO Chapter 11 Detailed Pivot Example
11 April Session 23	Node Potentials, and Reduced Arc Costs Continued. Spanning Trees and Basic Feasible Solutions Cramer's Rule	AMO Chapter 11
13 April Session 24	Generalized Network Flows	AMPL model, data, and output
	Multicommodity Flows	Definition Examples AMPL: model and data files for examples 1 and 2 output
18 April Session 25	Multicommodity Flows Continued Network Flow Problems with Fixed Costs: Example 1 Network Flow Problems with Fixed Costs: Example 2	AMPL Files model file data file
29 April Session 26	The Ratio Test Review of the Network Simplex Algorithm Node Potentials, and Reduced Arc Costs	AMO Chapter 11 Detailed Pivot Example
25 April Session 27	Optimal Trees	AMO Chapter 13
27 April Session 28	Survivable Network Design	05-EMIS-02 AMPL run file data file
1 May Session 29	Survivable Network Design	Additional Notes
8 May	Final Exam	125 Caruth 3 PM to 6 PM