1. Lecture 1 (Part 1) Introduction/Overview Tuesday, 9/9/08
UMass Lowell Computer Science Analysis of Algorithms Prof. Karen Daniels Fall, 2008
Lecture 1 (Part 1)
Introduction/Overview
Tuesday, 9/9/08

2. Web Page
Web Page

3. Nature of the Course Core course: Advanced algorithms
Required for all CS Masters students
Algorithms doctoral qualifying exam is largely based on this course
Advanced algorithms
Builds on undergraduate algorithms
No programming required
“Pencil-and-paper” exercises
Lectures supplemented by:
Programs
Real-world examples

4. What’s It All About? Algorithm:
steps for the computer to follow to solve a problem
Some of our goals:(at an advanced level)
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 Shortest Path Fourier Transform Bin Packing
Input: Edge-weighted graph G, with start vertex s and end vertex t
Problem: Find the shortest path from s to t in G
Bin Packing
Input: A set of n items with sizes d_1,...,d_n. A set of m bins with capacity c_1,...,c_m.
Problem: How do you store the set of items using the fewest number of bins?
Fourier Transform
Input: A sequence of n real or complex values h_i, 0 <= i <= n-1, sampled at uniform intervals from a function h.
Problem: Compute the discrete Fourier transform H of h
Nearest Neighbor
Input: A set S of n points in d dimensions; a query point q.
Problem:Which point in S is closest to q?
SOURCE: Steve Skiena’s Algorithm Design Manual
(for problem descriptions, see graphics gallery at

7. Some Typical Problems Transitive Closure Eulerian Cycle Edge Coloring
Input: A directed graph G=(V,E).
Problem: Construct a graph G'=(V,E') with edge (i,j) in E' iff there is a directed path from i to j in G. For transitive reduction, construct a small graph G'=(V,E') with a directed path from i to j in G' iff (i,j) in E.
Convex Hull
Input: A set S of n points in d-dimensional space.
Problem: Find the smallest convex polygon containing all the points of S.
Eulerian Cycle
Input: A graph G=(V,E).
Problem: Find the shortest tour of G visiting each edge at least once.
Edge Coloring
Input: A graph G=(V,E).
Problem: What is the smallest set of colors needed to color the edges of E such that no two edges with the same color share a vertex in common?

8. Some Typical Problems Hamiltonian Cycle Clique Input: A graph G=(V,E).
Problem: Find an ordering of the vertices such that each vertex is visited exactly once.
Clique
Input: A graph G=(V,E).
Problem: What is the largest S that is a subset of V such that for all x,y in S, (x,y) in E?

9. Tools of the Trade: Core Material
Algorithm Design Patterns
dynamic programming, linear programming, greedy algorithms, approximation algorithms, randomized algorithms, sweep algorithms, (parallel algorithms)
Advanced Analysis Techniques
amortized analysis, probabilistic analysis
Theoretical Computer Science principles
NP-completeness, NP-hardness
Asymptotic Growth of Functions
Summations
Recurrences
Sets
Probability
MATH
Proofs
Calculus
Combinations
Logarithms
Number Theory
Geometry
Trigonometry
Complex Numbers
Permutations
Linear Algebra
Polynomials

10. Asymptotic Growth of Functions
Prerequisites or
Preferable co-requisite
Standard graduate-level prerequisites for math background apply.
Asymptotic Growth of Functions
Summations
Recurrences
Sets
Probability
MATH
Proofs
Calculus
Combinations
Logarithms
Number Theory
Geometry
Trigonometry
Complex Numbers
Permutations
Linear Algebra
Polynomials

11. 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
2nd Edition
Ordered for UML bookstore

12. Syllabus (current plan)
math quiz

13. Chapter Dependencies 2nd Edition
Math Review Appendices A, B, C: Summations, Proof Techniques (e.g. Induction), Sets, Graphs, Counting & Probability
Ch 1-13 Foundations
Ch 22-24,25,26
Graph Algorithms
Ch 15, 16, 17
Advanced Design &
Analysis Techniques
Ch 35 Approximation Algorithms
Ch 34
NP-Completeness
Ch 29
Linear Programming
Math: Linear Algebra
2nd Edition
Ch 33
Computational Geometry
Math: Geometry (High School Level)
Ch 31
Number-Theoretic Algorithms RSA
Math: Number Theory
Ch 32
String Matching
Automata

14. Important Dates Math Quiz: Tuesday, 9/16 Midterm Exam: Tuesday, 10/21
In class
Closed book, no calculators
Midterm Exam: Tuesday, 10/21
Open book, open notes
Final Exam: to be determined

15. Grading Homework 30% Midterm 30% (open book, notes )
Final Exam 35% (open book, notes )
Instructor’s Discretion 5%

16. Homework HW# Assigned Due Content
1 T 9/9 T 9/ review & Chapter 15