Graphs and Network Flows
IE411
Lecture 1
Dr. Ted Ralphs
IE411 Lecture 1
1
References for Todays Lecture
Required reading
Sections 17.1, 19.1
References
AMO Chapter 1 and Section 2.1 and 2.2
IE411 Lecture 1
2
Introduction to Graphs and Network Flows
W
Graphs and Network Flows
IE411
Lecture 15
Dr. Ted Ralphs
IE411 Lecture 15
1
Preow-Push Algorithms
First developed by A. V. Goldberg in 1985.
Best preow-push algorithms outperform best augmenting path
algorithms in theory and in practice.
Push ows on in
Graphs and Network Flows
IE411
Lecture 14
Dr. Ted Ralphs
IE411 Lecture 14
1
Review: Labeling Algorithm
Pros
Guaranteed to solve any max ow problem with integral arc capacities
Provides constructive tool for establishing max-ow min-cut theorem
Cons
O(
Graphs and Network Flows
IE411
Lecture 12
Dr. Ted Ralphs
IE411 Lecture 12
1
References for Todays Lecture
Required reading
Sections 21.121.2
References
AMO Chapter 6
CLRS Sections 26.126.2
IE411 Lecture 12
2
Flows in Network
For the remainder of the
Graphs and Network Flows
ISE 411
Lecture 10
Dr. Ted Ralphs
ISE 411 Lecture 10
1
References for Todays Lecture
Required reading
Sections 21.3
References
AMO Chapter 5
CLRS Chapter 25
ISE 411 Lecture 10
2
Shortest Path Algorithms
Special structure eas
Graphs and Network Flows
ISE 411
Lecture 8
Dr. Ted Ralphs
ISE 411 Lecture 8
1
Why study shortest path problems?
They arise frequently in practice and as subproblems in higher-level
algorithms.
They are easy to solve eciently.
They capture most essentia
Graphs and Network Flows
IE411
Lecture 6
Dr. Ted Ralphs
IE411 Lecture 6
1
References for Todays Lecture
Required reading
Section 18.8
References
AMO Sections 3.4
CLRS Chapter 22
IE411 Lecture 6
2
General Graph Search
Depth-rst search is so called be