CS 5321:
Advanced Algorithms Median/
Order Statistics Algorithms
Ali Ebnenasir
Department of Computer Science
Michigan Technological University
Selection Problem
Input: A set of n distinct numbers and and
integer 1 <= k <= n
Acknowledgement
Eric Torng
CS 5321:
Advanced Algorithms
Greedy Algorithms
Ali Ebnenasir
Department of Computer Science
Michigan Technological University
Greedy Algorithms
Basic idea
Theoretical foundation (Matroids)
Connection to dynamic programming
Proof Techniques
Acknowledgemen
CS 5321:
Advanced Algorithms
Probabilistic Analysis &
Randomized Algorithms
Ali Ebnenasir
Department of Computer Science
Michigan Technological University
Outline
Tools from probability theory
Example: indicator random variables, expected value, linear
Acknowledgement
CS 5321:
Advanced Algorithms Sorting
Ali Ebnenasir
Department of Computer Science
Michigan Technological University
Outline
Heapsort
Quicksort
Quick review of basic sorting methods
Lower bounds for comparison-based
methods
Non-comparison
Motivations
CS 5321:
Advanced Algorithms
Amortized Analysis
Why amortized analysis and when?
Suppose you have a linked list of sorted
elements
How difficult is it to find min/max?
If you do not allow insert/delete operations
on your data structure, t
CS 5321:
Advanced Algorithms Objectives
Acknowledgement
Eric Torng
Moon Jung Chung
Charles Ofria
Dr. Ali Ebnenasir
Department of Computer Science
Michigan Technological University
1
Course Objectives
2
Outline
What is a problem?
What is an algorithm?
CS 5321:
Advanced Algorithms
Analysis Using Recurrence
Dr. Ali Ebnenasir
Department of Computer Science
Michigan Technological University
Outline
Acknowledgement
Eric Torng
Moon Jung Chung
Charles Ofria
Example: Towers of Hanoi
Recursive algorithms v
8/31/15
Outline
CS 5321:
Advanced Algorithms Introduction
Course info
Instructor info
Course outline
Teaching philosophy
Dr. Ali Ebnenasir
Department of Computer Science
Michigan Technological University
Grading
Homework
Exams
1
2
Course Info
Instr
CS 5321:
Advanced Algorithms
Proof Techniques
Ali Ebnenasir
Department of Computer Science
Michigan Technological University
Deductive Reasoning
The conclusion is derived from a set of previously
known facts
The premises necessitate the conclusion
Als
CS 5321:
Advanced Algorithms Analysis
Acknowledgement
Eric Torng
Moon Jung Chung
Charles Ofria
Dr. Ali Ebnenasir
Department of Computer Science
Michigan Technological University
1
2
Modeling Algorithms
Analyzing Algorithms
RAM model of computation
Inpu