This section contains documents that could not be made accessible to screen reader software. A "#" symbol is used to denote such documents.
Although some of the lecture below were scribed during the 2005 version of this course, many of the scribed notes below are from previous versions of the course. These older notes were made available to the students.
Scribed notes were taken by the students and used with permission.
The instructor notes often span several lectures
Lecture notes files.
| LEC # |
TOPICS |
SCRIBE NOTES |
Instructor NOTES |
| 1 |
Course Introduction
Fibonacci Heaps |
Fibonacci Heaps (PDF) (Courtesy of David Andersen, Ioana Dumitriu, John Dunagan, and Akshay Patil.) |
(PDF 1)
(PDF 2) |
| 2 |
MST
Persistent Data Structures |
Persistent Data Structures (PDF) (Courtesy of Sommer Gentry and Eddie Kohler.) |
(PDF) |
| 3 |
Splay Trees |
Splay Trees (PDF) (Courtesy of Xin Zhang.) |
(PDF) |
| 4 |
Splay Trees (cont.)
Suffix Trees
Tries |
Suffix Trees and Fibonacci Heaps (PDF) |
(PDF) |
| 5 |
Suffix Trees (cont.)
Tries (cont.)
Dial's Algorithm |
|
|
| 6 |
Dijkstra's Algorithm
Van Emde Boas Queues |
Van Emde Boas Queues (PDF)# (Courtesy of Abhi Shelat, Andrew Menard, and Akshay Patil.) |
(PDF) |
| 7 |
Van Emde Boas Queues (cont.)
Hashing |
|
(PDF) |
| 8 |
2-Level Hashing
Network Flows |
Maximum Flows (PDF) (Courtesy of Alexandr Andoni.) |
(PDF) |
| 9 |
Network Flows: Augmenting Paths, Maximum Augmenting Paths, Scaling |
|
|
| 10 |
Reductions between Flow Problems
Bipartite Matching
Shortest Augmenting Path
Blocking Flows |
|
|
| 11 |
Blocking Flows (cont.) |
|
|
| 12 |
Min-Cost Flows |
Min-Cost Flow Algorithms (PDF) (Courtesy of Wendy Chang.) |
(PDF) |
| 13 |
Min-Cost Flows (cont.)
Linear Programming |
|
(PDF) |
| 14 |
Linear Programming (cont.)
Structure of Optima
Weak Duality |
Duality (PDF) (Courtesy of Jay-Kumar Sundararajan.) |
|
| 15 |
Linear Programming (cont.)
Strong Duality |
Duality(PDF) (Courtesy of Jay-Kumar Sundararajan.) |
|
| 16 |
Linear Programming (cont.)
Complementary Slackness
Algorithms: Simplex, Ellipsoid |
Duality (PDF) (Courtesy of Jay-Kumar Sundararajan.) |
|
| 17 |
Linear Programming (cont.)
Algorithms: Interior Point |
|
|
| 18 |
Approximation Algorithms
NP-hard problems |
|
(PDF) |
| 19 |
4/3-Approximation for TSP |
|
|
| 20 |
Relaxations
Directed TSP |
|
|
| 21 |
Randomized Rounding
Chernoff Bound
Fixed Parameter Tractability
Kernelization |
|
(PDF) |
| 22 |
Online Algorithms (Ski Rental, Load Balancing, Paging) |
Lower Bounds for Competitive Ratios of Randomized
Online Algorithms (PDF) (Courtesy of Chun-Chieh Lin.) |
(PDF) |
| 23 |
Randomized Online Algorithms (Adversaries, Fiat's Marking Algorithm, Potential Functions, Yao's Minimax Principle) |
Lower Bounds for Competitive Ratios of Randomized
Online Algorithms (PDF) (Courtesy of Chun-Chieh Lin.) |
|
| 24 |
K-Server Problem
Double-Coverage Algorithm
Computational Geometry Introduction (Orthogonal Range Search) |
|
|
| 25 |
Sweep Algorithms (Convex Hull, Segment Intersection, Voronoi Diagrams) |
Sweep Line (PDF) (Courtesy of Matt Rasmussen.) |
(PDF) |
| 26 |
Sweep Algorithms (Voronoi Diagrams)
Randomized Incremental Constructions
Backwards Analysis
Linear Programming in Fixed Dimension |
|
|
| 27 |
(Optional Material) External Memory Algorithms |
|
(PDF) |
| 28 |
(Optional Material) Cache Oblivious Algorithms: Matrix Multiplication, Linked Lists, Median |
|
|
| 29 |
(Optional Material) Cache Oblivious Algorithms: Search
Streaming Model |
|
|
| 29 |
(Optional Material) Parallel Algorithms
|
|
(PDF) |
Lecture notes from the 2004 version of this course.
Course lectures.
| LEC # |
TOPICS |
SCRIBE NOTES |
| 1 |
Course Introduction
Fibonacci Heaps |
(PDF)# Courtesy of David Andersen, Ioana Dumitriu, John Dunagan, and Akshay Patil.) |
| 2 |
Persistent Data Structures
Suffix Trees |
(PDF 1) (Courtesy of Sommer Gentry and Eddie Kohler.)
(PDF 2) (Courtesy of Jiawen Chen.) |
| 3 |
Suffix Trees (cont.) |
(PDF)# |
| 4 |
Treaps |
|
|
Splay Trees |
(PDF) (Courtesy of Naveen Sunkavally.) |
| 5 |
Hashing: 2-Universal, Perfect Hashing
Fingerprinting |
|
| 6 |
Fingerprinting (cont.)
Max Flows |
(PDF 1) (Courtesy of Jiawen Chen.)
(PDF 2) (Courtesy of Alexandr Andoni.) |
| 7 |
Max Flows (cont.) |
|
| 8 |
Max Flows (cont.) |
|
| 9 |
Max Flows (Max Flow of Min Cost) |
|
|
Dynamic Trees
Preflow-push Algorithm |
|
| 10 |
Min Cost Flow Algorithms
Linear Programming |
(PDF 1)# (Courtesy of Brian Dean and John Jannotti.) |
| 11 |
Linear Programming (cont.)
Farkas Lemma
Duality |
(PDF)# (Courtesy of Vinod Vaikuntanathan.) |
|
Goldberg-Tarjan Min-cost Flow |
(PDF)# (Courtesy of Mohammad Hajiaghayi and Vahab Mirrokni.) |
| 12 |
Linear Programming: More Duality (Weak and Strong Duality)
Complementary Slackness Conditions |
|
| 13 |
Linear Programming: Complementary Slackness Conditions (Same Scribes as Above) |
|
| 14 |
LP: Interior Points Algorithm
Approximation Algorithms: Constant, Relative Approximation |
(PDF)# (Courtesy of Jason Eisenberg.) |
| 15 |
Approximation Algorithm: PAS, FPAS, Rounding, Enumeration |
|
| 16 |
Approximation Algorithm: Rounding, Relaxation |
(PDF)# (Courtesy of Sachin Katti.) |
| 17 |
Approximation Algorithm: LP Relaxation, Randomized Rounding |
(PDF)# (Courtesy of Shannon McDonald.) |
| 18 |
Fixed Parameter Tractability |
(PDF)# (Courtesy of Shannon McDonald.) |
| 19 |
Fixed Parameter Tractability - Treewidth
Online Algorithms |
|
| 20 |
Online Algorithms (cont.): Paging, Randomization, Potential Functions |
|
| 21 |
Randomized Online Algorithms (Adversarial Models, Marking Algorithm) |
|
| 22 |
Lower Bounds for Randomized Online Algorithms
Geometry: Range Search |
(PDF)# (Courtesy of Nick Harvey.) |
| 23 |
Convex Hulls
Voronoi Diagrams |
|
| 24 |
Voronoi Diagrams (cont.)
Randomized Incremental Construction: Binary Space Partition |
|
| 25 |
Backwards Analysis for RIC: Convex Hull, Linear Programming |
|
| 26 |
External Memory Algorithms |
|
| 27 |
Cache-oblivious Algorithms |
|