CSC 323 Algorithm Design and Analysis, Spring 2015

Instructor: Dr. Natarajan Meghanathan

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Syllabus
Lecture Slides
Project Descriptions
Dr. Meg's Desktop Selected Lecture Videos
Quiz, Exam and Project Schedules
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Syllabus

CSC 323 Syllabus, Spring 2015

Lecture Slides

Module 1: Algorithm Efficiency Analysis

Module 2: Classical Design Techniques

Module 3: Greedy Strategy

Module 4: Dynamic Programming

Module 5: Graph Theory Algorithms

Module 6: NP Complete Problems and Approximation Heuristics

 

Project Descriptions

Project 1: Element Uniqueness Problem, Due: Feb. 12

Project 2: Comparing the Performance of a Recursive vs. a Non-Recursive Algorithm to Determine the Index of the Element with the Largest Value in an Array, Due: Feb. 19

Project 3: Computing the Number of Paths of a Certain Length in a Graph using Matrix Multiplication, Due: March 5

Project 4: Determining the Common Elements across All Arrays using Hash Tables and Java Collection Classes

Video Explanation: Vector Example        Video Explanation: TreeMap Example

Project 5: Coin Collection Problem using Dynamic Programming

Project 6: Theorem Proving Project: Bloom Filters, Breadth First Search and Asymptotic Complexity

Project 7: Theorem Proving Project: Topological Sort (DAG), Dijkstra Algorithm and Bellman-Ford Algorithm

 

 

Dr. Meg's Desktop Selected Lecture Videos (YouTube Links)

Module 1 (Chapter 2): Analyzing the Efficiency of Algorithms

Time-Complexity analysis of a recursive algorithm to compute the factorial of an integer    

Example for solving recurrence relations    

Time-complexity analysis of an iterative algorithm to determine whether an array has unique elements    

Time-Complexity analysis of a recursive algorithm to determine the number of bits needed to represent a positive integer    

Module 2 (Chapters 3-6): Classical Algorithm Design Techniuqes

Brute Force Algorithms QB – String Matching Problems

Decrease and Conquer – Insertion Sort Algorithm and Examples

Divide and Conquer – Theorem-Proof: In order Traversal of a Binary Search Tree

Divide and Conquer – Master Theorem

Binary Search Algorithm and Examples

Comparison of Bottom-up and Top-down Approaches for Heap Construction    

Transform and Conquer – Proof for Euclid's GCD Formula

Transform and Conquer – Heap Sort

Space-Time Tradeoffs for the Sorting Algorithms (Merge, Insertion and Heap Sorts)    

Module 3 (Chapter 9): Greedy Technique

Greedy Technique – Fractional Knapsack Problem

Greedy Technique – Huffman Codes (Variable Length Prefix-free Encoding)

Module 4 (Chapter 8): Dynamic Programming

Dynamic Programming: Coin-row Problem Discussion and Example

Dynamic Programming: Binomial Coefficient

Dynamic Programming: Coin-Collecting Problem for a Robot in a Two-dimensional Grid

Dynamic Programming: Integer Knapsack Problem (0-1 Knapsack Problem)

Module 5: Graph Theory Algorithms

Depth First Search on Directed Graph

Depth First Search and Articulation Points

Breadth First Search and 2-Colorability of Graphs

Topological Sort on DAGs and Proof for Neccessary and Sufficient Condition

Dijkstra's Algorithm for Shortest Path Trees and Proof for Correctness

Bellman-Ford Algorithm for Shortest Path Trees and Examples New!!

Kruskal's Algorithm: Examples to find Minimum Spanning Trees

Kruskal's Algorithm: Proof of Correctness

Properties (1 and 2) of Minimum Spanning Tree: IJ-Cut and Minimum Weight Edge

Properties (3 and 4) of Minimum Spanning Tree: A graph with unique edge weights has only one minimum spanning tree

Property 5 of Minimum Spanning Tree: Given a graph with unique edge weights, the largest weight edge in any cycle cannot be part of any minimum spanning tree

Prim's Algorithm for Minimum Spanning Trees and Proof for Correctness

Floyd's All Pairs Shortest Paths Algorithm
Part 1     Part 2     Part 3     Part 4     Part 5     Part 6     Part 7    

Module 6: P, NP and NP-Complete Problems

Polynomial Reduction: Hamiltonian Circuit to Traveling Salesman Problem    

Minimal Number of Uncovered Neighbors Heuristic: Example to determine an Independent Set, Vertex Cover and Clique    

Polynomial Reductions: Independent Set, Clique and Vertex Cover    

Multi-fragment Heuristic for the Traveling Salesman Problem    

Twice around the tree Heuristic for the Traveling Salesman Problem and the Proof for approximation ratio    

Quiz, Exam and Project Schedules