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Lecture Notes

Combinatorial Algorithms

12 years 11 months ago
Combinatorial Algorithms
"This is a standard senior-level algorithms class required of every computer science undergraduate and graduate student at the University of Illinois."
Jeff Erickson
Added 13 Feb 2009
Updated 13 Feb 2009
Year 2006
Authors Jeff Erickson
Background
Notes on solving recurrences
0. Introduction
1. Divide and conquer
2. Dynamic programming
Randomized algorithms
3. Randomization: Nuts and bolts
4. Randomized treaps
5. Randomized mincut
6. Uniform and universal hashing
A. Skip lists
Amortized analysis
7. Amortized analysis
8. Scapegoat trees and splay trees
9. Union-find
Fibonacci heaps
Graph algorithms
10. Representing and searching graphs
11. Single-source shortest paths
12. All-pairs shortest paths
13. Minimum spanning trees
Seminumerical algorithms
14. Fast Fourier transforms
15. Number-theoretic algorithms
String matching
C. String matching: Rabin-Karp
D. String matching: Knuth-Morris-Pratt
Computational Geometry
E. Convex hulls
F. Plane sweep algorithms
G. Polygon triangulation
Lower bounds
H. Information theory
I. Adversary arguments
J. Reductions and transformations
16. NP-hard, NP-easy, and NP-complete problems 
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