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(See below for color codes for credits for lecture notes.) |
Readings
(from [CLRS] unless otherwise noted)
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Introduction:
Auxiliary
Notes:
Introduction
to Algorithms ps
pdf Optional
Notes:
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Required:
Optional: [GKP, 1.1-1.2]
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Asymptotic
Analysis:
Auxiliary
Notes:
Growth
of functions, summations ps
pdf Optional Notes: |
Required:
Optional:
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Mathematical
foundations:
Auxiliary
Notes:
Strassen's
algorithm, Master method for recurrence ps
pdf Optional Notes: |
Required:
Optional: [CLRS 28.1-28.2] |
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| Wend Jan 15 | Review Lecture on Recurrence Equations | ||||
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Quiz
on Recurrence Equations and Asymptotics
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Wend Jan 22 |
Overview of Randomized and Average-Case Analysis
Probabilistic Algorithms ps pdf Auxiliary Notes: |
Required:
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Sorting:
Introduction to Quicksort ps pdf Applications of Sorting ps pdf Auxiliary
Notes:
Optional
Notes:
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Required:
Optional: [MR] |
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Priority
Queues:
Auxiliary
Notes:
Optional Notes: |
Required:
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Sorting:
Linear
time selection, median lower bound ps
pdf Deterministic Selection and Sorting ps pdf Optional
Notes:
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Required:
Optional: [Baase, 3.4] |
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Sorting:
Lower
bound in decision tree model, bucket and radix sort ps
pdf | ||||
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Quiz
on Recurrence Equations and Asymptotics (Optional)
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Searching:
Red-Black tree Rotation, Insertion, Deletion
ps pdf Search
trees, red-black trees ps
pdf Optional
Notes:
Example Red-Black tree problem ps pdf |
Required:
Optional: [CLRS
13,14] [deBerg, 10.1] |
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Searching:
Introduction to Hash Tables ps pdf Optional Notes: elementary data structures ps pdf |
Required:
Optional: [CLRS 8.4, 11] [GT, 7.5] |
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Mid
Term Exam postponed to WED FEB 19
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Mid
Term Exam on everything covered in the lectures after recursion and before
hashing. This includes Prob Analysis, Sorting, Selection, Searching, Lower
bounds for all above problems (No Hashing)
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| Mon Feb 24 |
Amortized
analysis, Part I:
Aggregate
analysis, potential method, binary counter, dynamic table ps
pdf Optional
Notes:
Amortized
analysis, Part II:
Optional
Notes:
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Required:
Optional: [Kozen, 12] |
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Graph
algorithms:
Graph Algorithms using Depth First Search
ps pdf Model,
basic algorithms, DFS, BFS, topological sort, strongly connected components
ps
pdf data structures for graphs ps pdf Auxiliary
Notes:
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Required:
Optional: [CLRS Appendix B.4-B.5] |
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Graph
algorithms:
Minimum
spanning trees, Union-Find ps
pdf Minimum Weights Spanning Tree ps pdf Data Structures for Disjoint Sets ps pdf Auxiliary
Notes:
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23,
21.0-21.3
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Graph
algorithms:
shortest path algorthms ps pdf Shortest Paths Problems ps pdf All-pairs Shortest Paths ps pdf Auxiliary
Notes:
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24.0-24.3,
25.2
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Graph
algorithms:
Auxiliary
Notes:
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26.2-26.3
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Graph
Algorithms:
Flow Networks, continued ps pdf Auxiliary
Notes:
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26.0-26.2
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Review
Lecture on Graph Algorithms
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Mid
Term Exam on Amortized Analysis and all Graph related topics covered till date
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Wed
April 2
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External
memory algorithms:
Model,
basic upper and lower bounds, sorting, B-trees ps
pdf Auxiliary
Notes:
[Vitter]
The Input/Output Complexity of Sorting and Related Problems pdf,
Arge:
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Required:
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Design
paradigms:
Dynamic
programming Matrix chain multiplication ps
pdf introduction to dynamic programming ps pdf dynamic programming applications ps pdf Auxiliary
Notes:
Example dynamic programming problem ps pdf |
Required:
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| Mon April 7 |
Design
paradigms:
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Required:
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Fast
Fourier Transform:
Polynomials and the Fast Fourier Transform
ps pdf Auxiliary
Notes:
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30
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Number
Theory and Cryptography Algorithms:
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31
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Approximation
Algorithms:
Approximation
Algorithms ps
pdf Approximately Correct Algorithms ps pdf Auxiliary
Notes:
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35.0-35.3
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Review
of the Course Material
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Thur May 1
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Final
Exam (2 p.m.-5 p.m.)
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