1. Lecture 1 Introduction/Overview Text: Chapters 1, 2 Wed. 1/28/04
UMass Lowell Computer Science Analysis of Algorithms Prof. Karen Daniels Spring, 2004
Lecture 1
Introduction/Overview
Text: Chapters 1, 2
Wed. 1/28/04

2. Web Page
Web Page

3. Nature of the Course Core course: required for all CS majors
Advanced undergraduate level
Graduate students take separate course (91.503)
No programming required
“Pencil-and-paper” exercises
Lectures supplemented by:
Programs
Real-world examples

4. What’s It All About? Algorithm: Some of our goals:
steps for the computer to follow to solve a problem
well-defined computational procedure that transforms input into output
Some of our goals:
recognize structure of some common problems
understand important characteristics of algorithms to solve common problems
select appropriate algorithm to solve a problem
tailor existing algorithms
create new algorithms

5. Some Algorithm Application Areas
Computer Graphics
Geographic
Information Systems
Robotics
Bioinformatics
Astrophysics
Medical Imaging
Telecommunications
Design
Apply
Algorithms
Analyze

6. Some Typical Problems Sorting Minimum Spanning Tree Median finding
Input: Set of items
Problem: Arrange items “in order”
Median finding
Input: Set of numbers or keys
Problem: Find item smaller than half of items and bigger than half of items
Minimum Spanning Tree
Input: Graph G = (V,E) with weighted edges
Problem: Find subset of E of G of minimum weight which forms a tree on V
Shortest Path
Input: Edge-weighted graph G , with start vertex and end vertex t
Problem: Find the shortest path from to t in G
SOURCE: Steve Skiena’s Algorithm Design Manual
(for problem descriptions, see graphics gallery at

7. Tools of the Trade Algorithm Design Patterns such as:
divide-and-conquer
Data Structures such as:
trees, linked lists, hash tables, graphs
Algorithm Analysis Techniques such as:
asymptotic analysis
probabilistic analysis
Growth of Functions
Summations
Recurrences
Sets
Probability
MATH
Proofs
Logarithms
Permutations
Combinations

8. Tools of the Trade: (continued) Algorithm Animation

9. What are we measuring? Some Analysis Criteria: Scope “Dimension”
The problem itself?
A particular algorithm that solves the problem?
“Dimension”
Time Complexity? Space Complexity?
Type of Bound
Upper? Lower? Both?
Type of Input
Best-Case? Average-Case? Worst-Case?
Type of Implementation
Choice of Data Structure

10. Prerequisites Computing I (91.101) Computing II (91.102)
Discrete Math I & II (92.321, )
Statistics for Scientists and Engineers (92.386)
Calculus I-III ( )
Growth of Functions
Summations
Recurrences
Sets
Probability
MATH
Proofs
Logarithms
Permutations
Combinations

11. Course Structure: 4 Parts
Foundations
Analyzing & Designing Algorithms, Growth of Functions, Recurrences, Probability & Randomized Algorithms
Sorting
Heapsort, Priority Queues, Quicksort, Sorting in Linear Time
Data Structures
Stacks and Queues, Linked Lists, Introduction to Trees, Hash Tables, Binary Search Trees, Balancing Trees: Red-Black Trees
Graph Algorithms
DFS, BFS, Topological Sort, MST, Shortest paths
Part 1
Part 2
Part 3
Part 4

12. Textbook Required: Introduction to Algorithms
by T.H. Corman, C.E. Leiserson, R.L. Rivest
McGraw-Hill
2001
ISBN
see course web site (MiscDocuments) for errata (1st edition)
New Edition
Ordered for UML bookstore

13. Syllabus (current plan)
Syllabus (current plan)
Lecture Date
Topic
Reading
Foundations
Chapters 1-5
W 1/28
Introduction/Overview
Chapter 1
F 1/30, M 2/2, W 2/4
Analyzing & Designing Algorithms
Chapter 2
F 2/6, M 2/9, W 2/11
Growth of Functions
Chapter 3
F 2/13, W 2/18, Th 2/19
Recurrences
Chapter 4
F 2/20, M 2/23, W 2/25
Probability & Randomized Algorithms
Chapter 5
Sorting
Chapters 6-9
F 2/27, M 3/1
Heapsort/ Priority Queues
Chapter 6
W 3/3, F 3/5
Quicksort
Chapter 7
M 3/8, W 3/10
Review
F 3/12
Midterm Exam
M 3/22
W 3/24, F 3/26, M 3/29
Sorting in Linear Time
Chapter 8
Data Structures
Chapters 10-13
W 3/31, F 4/1, M 4/5
Stacks, Queues, Linked Lists, Trees
Chapter 10
W 4/7, F 4/9
Hash Tables
Chapter 11
M 4/12, W 4/16, F 4/18
Binary Search Trees
Chapter 12
W 4/21, F 4/23
Balancing Trees: Red-Black Trees
Chapter 13
Graph Algorithms
Chapters 22-24
M 4/26, W 4/28, M 5/3
Elementary Graph Algorithms
Chapter 22
W 5/5, F 5/7
Minimum Spanning Trees
Chapter 23
M 5/10
Shortest Paths
Chapter 24
W 5/12, F 5/14
1-13, 15-16, 22-24
To Be Determined
Final Exam
Revised for Fall, 2001 in accordance with ACM Computer Science Computing Curricula 2001, Steelman Draft, August, 2001.

14. CS Theory Math Review Sheet The Most Relevant Parts...
O, Q, W definitions
Series
Combinations
p. 2 Recurrences & Master Method
p. 3
Probability
Factorial
Logs
Stirling’s approx
p. 4 Matrices
p. 5 Graph Theory
p. 6 Calculus
Product, Quotient rules
Integration, Differentiation
Logs
p. 8 Finite Calculus
p. 9 Series
Math fact sheet (courtesy of Prof. Costello) is on our web site.

15. Important Dates Midterm Exam (Chapters 1-5): Friday, 3/12
Final Exam: TBA

16. Grading Homework 35% Midterm (Chapters 1-5) 30% (open book, notes )
Final Exam 35% (open book, notes )