Stanford Open Classrooms – Design & Analysis of Algorithms 2011

Stanford Open Classrooms – Design & Analysis of Algorithms 2011 2011 | English | 12.85 GB | DVD
Genre: E-Learning
Course Overview: Introduction to basic techniques for design and analysis of algorithms, including asymptotic analysis, divide and conquer algorithms and recurrences, greedy algorithms, data structures, dynamic programming, graph algorithms and randomized algorithms.

REQUIRED TEXTBOOK: Kleinberg and Tardos, Algorithm Design, 2005. We will cover most of Chapters 4-6, parts of Chapter 13, and a couple of topics that had not the book.

Prerequisites: Introduction to evidence and discrete mathematics and probability (eg, CS 103 and Stat116). If you have not taken a course in probability, you should expect to do independent reading during the race on topics such as random variables, expectation, conditioning, and basic combinatorics.

1. INTRODUCTION (1/4/2011)
Why are you here
Example: Internet Routing
Shortest-Path Algorithms
Example: Sequence Alignment (Part 1)
Example: Sequence Alignment (Part 2)
Beating Brute Force Search
Administrivia
Recursive Algorithms for Integer Multiplication
Gauss’s Trick

2. BASIC DIVIDE, and CONQUER (1/6/2011)
Merge Sort: Motivation
Merge Sort: Formal Definition
Running Time of Merge
Running Time of Merge Sort (Part 1)
Running Time of Merge Sort (Part 2)
Guiding Principles of CS161 (Part 1)
Guiding Principles of CS161 (Part 2)
Review of Asymptotic Notation
Asymptotic Notation: Example #1
Asymptotic Notation: Example #2
Big-Omega, and Big-Theta

3. THE MASTER METHOD (1/11/2011)
Integer Multiplication Revisited
Master Method: Formal Statement (Part 1)
Master Method: Formal Statement (Part 2)
Master Method: Examples
Proof of Master Method (Part 1)
Proof of Master Method (Part 2)
Master Method: Interpretation of the Three Cases
Proof of Master Method (Part 3)

4. LINEAR-TIME MEDIAN (1/13/2011) – We apologize for the poor audio quality in this video.
The Selection Problem
Partitioning Around a Pivot
A Generic Selection Algorithm
Median of Medians
Recap
Rough Recurrence
Key Lemma (Part 1)
Key Lemma (Part 2)
The Substitution Method
Analysis of Rough Recurrence

5. GRAPH SEARCH, and DIJKSTRA’S ALGORITHM (1/18/2011)
Graph Primitives
Representing Graphs: Adjacency Matrices, and Lists
Breadth-First, and Depth-First Search
Dijkstra’s Algorithm (Part 1)
Dijkstra’s Algorithm (Part 2)
Dijkstra’s Algorithm: Example
Dijkstra’s Algorithm: Proof of Correctness (Part 1)
Dijkstra’s Algorithm: Proof of Correctness (Part 2)
Undirected Connectivity

6. CONNECTIVITY IN DIRECTED GRAPHS (1/20/2011)
Strongly Connected Components
SCCs: A Two-Pass Algorithm
Depth-First Search Revisited
Example (Part 1)
Example (Part 2)
Two-Tier Structure of Directed Graphs
Correctness of Algorithm
Correctness Intuition
Proof of Key Lemma
Structure of the Web, Small World Property, and PageRank

7. INTRODUCTION TO GREEDY ALGORITHMS (1/25/2011)
Course Roadmap
Application, and Final Exam Info
A Scheduling Problem
Two Greedy Algorithms
Correctness Proof
Cost-Benefit Analysis

8. MINIMUM SPANNING TREES (1/27/2011)
Introduction
Prim’s Algorithm
Graph Theory Preliminaries
Feasibility of Prim’s Algorithm
The Cut Property
Proof of Cut Property
Key Exchange Argument
Naive Running Time, and Heap Review
Implementing Prim with Heaps (Part 1)
Implementing Prim with Heaps (Part 2)
New Running Time Analysis

9. KRUSKAL’S ALGORITHM AND UNION-FIND (2/1/2011)
Kruskal’s Algorithm
Proof of Correctness (Part 1)
Proof of Correctness (Part 2)
Naive Running Time
Union-Find Data Structure
Union by Rank
Rank, and Size of Subtrees
Open Research Question
Path Compression
Path Compression, and the Ackermann Function

10. PATH COMPRESSION AND CLUSTERING (2/3/2011)
Union-Find Review
Path Compression
Rank Blocks
Counting Pointer Updates
Clustering
A Greedy Algorithm
Correctness of Greedy Algorithm (Part 1)
Correctness of Greedy Algorithm (Part 2)

11. INTRODUCTION TO RANDOMIZED ALGORITHMS (2/8/2011)
The Min Cut Problem
The Contraction Algorithm
Probability Review
Analysis of Contraction Algorithm
Success Through Independent Trials
Final Comments

12. QUICKSORT (2/10/2011)
The QuickSort Algorithm
Best-Case, and Worst-Case Pivots
Running Time of Randomized QuickSort
Probability Review Part 2
Linearity of Expectation
Counting Comparisons
Crux of Proof
Final Calculations
Lower Bound of Comaprison-Based Sorting

13. HASHING (2/15/2011)
Hashing: Introduction
Hashing: High-Level Idea
Running Time
How to Analyze Hashing
Universal Hashing
Proof of O(1) Running Time
A Universal Family
Universality: Proof Idea
Bloom Filters

14. BALANCED SEARCH TREES AND SKIP LISTS (2/17/2011)
Review of Binary Search Trees
Deleting from a BST
Red-Black Trees
Height of Red-Black Trees
Rotations
Insertion to a Red-Black Tree
Skip Lists: High-Level Idea
Skip Lists: Intuition for Analysis

15. INTRODUCTION TO DYNAMIC PROGRAMMING (2/22/2011)
Dynamic Programming: A First Example
Structure of Optimal Solution
A Recursive Algorithm
Bottom-Up Formulation
Reconstruction Algorithm
The Knapsack Problem
Dynamic Programming Solution

16. SEQUENCE ALIGNMENT (2/24/2011)
Sequence Alignment
Optimal Substructure
Dynamic Programming Solution
Dynamic Programming Algorithm
Shortest Paths with Negative Edge Lengths
On Negative Cycles
Optimal Substructure (Part 1)
Optimal Substructure (Part 2)

17. SHORTEST PATHS: BELLMAN-FORD AND FLOYD-WARSHALL (3/1/2011)
Single-Source Shortest Paths Revisited
The Bellman-Ford Algorithm
Negative Cycle Checking
Space Optimization
The Floyd-Warshall Algorithm (Part 1)
The Floyd-Warshall Algorithm (Part 2)
Dynamic Programming Algorithm

18. NP-COMPLETE PROBLEMS (3/3/2011)
Polynomial Time Algorithms, and P
The Traveling Salesman Problem
Reductions
Completeness
NP-Completeness
Many Problems are NP-Complete
Does P=NP
Coping with NP-Completeness
The Vertex Cover Problem
Smarter Brute-Force Search

19. APPROXIMATION ALGORITHMS (3/8/2011)
Performance Guarantees for Heuristics
A Greedy Knapsack Algorithm
Proof of Performance Guarantee
Final Exam Info
Better Performance via Dynamic Programming
Accuracy Analysis
Running Time Analysis

20. THE WIDER WORLD OF ALGORITHMS (3/10/2011)
Bipartite Matching
Stable Matching
Gale-Shapley Proposal Algorithm
Maximum Flow
Selfish Flow, and Braess’s Paradox
Linear Programming
Computational Geometry
Approximation, and Randomized Algorithms
Complexity, and Epilogue

7412d3e604e0648651bc4bb3f9fb2bf8 Stanford Open Classrooms – Design & Analysis of Algorithms 2011

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