Table of Contents
CSE 589 -- Lecture 2
Administrivia New and improved grading scheme:
Homework Turn-in
Plan for Today
Dynamic Programming
Example DP Problem: Matrix Chain Multiplication
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Dynamic Program for Matrix Chain Multiplication
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Homework problem Surface Reconstruction
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Graph algorithms discussed last time
New Topic Minimum Spanning Trees
Prim’s algorithm
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Priority Queue
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Kruskal’s algorithm
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Disjoint Set Data Structure Union/Find
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New Topic: Shortest Paths
Dijkstra’s algorithm
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Shortest paths with negative weights
All-pairs shortest paths Floyd-Warshall
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New Topic: Maximum Flow
Max-flow outline:
Properties of Flow: f(v,w) -- flow on edge (v,w)
An augmenting path with respect to a given flow f is a
Using an augmenting path to increase flow
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Augmenting Path Theorem: A flow f is maximum iff it admits no augmenting path
=> Celebrated Max-flow Min-Cut Theorem
Residual Graph w.r.t. flow f
Ford-Fulkerson Method (G,s,t)
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Edmonds-Karp
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Fastest max-flow algorithms: preflow-push
Preflow-push algorithms
Some applications of max-flow and max-flow min-cut theorem
Bipartite Matching
Network Connectivity
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Scheduling on uniform parallel machines
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Shipping Problem
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Problems
Problems
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