Title: UMass%20Lowell%20Computer%20Science%2091.503%20Analysis%20of%20Algorithms%20Prof.%20Karen%20Daniels%20Spring,%202005
1UMass Lowell Computer Science 91.503 Analysis
of Algorithms Prof. Karen Daniels Spring, 2005
- Lecture 1 (Part 1)
- Introduction/Overview
- Tuesday, 1/25/05
2Web Page
Web Page
http//www.cs.uml.edu/kdaniels/courses/ALG_503.h
tml
3Nature of the Course
- Core course required for all CS graduate
students - Advanced algorithms
- Builds on undergraduate algorithms 91.404
- No programming required
- Pencil-and-paper exercises
- Lectures supplemented by
- Programs
- Real-world examples
4Whats 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
5Some Algorithm Application Areas
6Some Typical Problems
Shortest Path 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 lt i lt 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. - ProblemWhich point in S is closest to q?
SOURCE Steve Skienas Algorithm Design Manual
(for problem descriptions, see graphics gallery
at http//www.cs.sunysb.edu/algorith)
7Some Typical Problems
- Transitive Closure
- 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?
8Some Typical Problems
Hamiltonian Cycle 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?
9Tools 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
10Prerequisites
- 91.500 and 91.404 or 91.583.
- Co-requisite 91.502.
- Standard graduate-level prerequisites for math
background apply.
11Textbook
- Required
- Introduction to Algorithms
- by T.H. Corman, C.E. Leiserson, R.L. Rivest
- McGraw-Hill
- 2001
- ISBN 0-07-013151-1
- see course web site (MiscDocuments) for errata
New Edition
Ordered for UML bookstore
12Syllabus (current plan)
13Chapter Dependencies
Math Review Appendices A, B, C Summations, Proof
Techniques (e.g. Induction), Sets, Graphs,
Counting Probability Ch 1-13 Foundations
Ch 35 Approximation Algorithms
Ch 34 NP-Completeness
Ch 29 Linear Programming
Math Linear Algebra
New Edition
Ch 33 Computational Geometry
Math Geometry (High School Level)
Ch 31 Number-Theoretic Algorithms RSA
Math Number Theory
Ch 32 String Matching
Automata
14Important Dates
- Midterm Exam Tuesday, 3/22 in class
- In class
- Open book, open notes
- Final Exam to be determined
15Grading
- Homework 35
- Midterm 30 (open book, notes )
- Final Exam 35 (open book, notes )
16Homework
HW Assigned Due Content
- 1 T 1/25 T 2/1 91.404 review
Chapter 15 -
17ISET Research Scholars Program
Information Sciences, Engineering and Technology
- Selected Research Project Areas
- Telecommunications
- Wireless Networks
- Network Performance
- Systems
- Multimedia Systems
- Acoustics
- Computer Science
- Network Security
- Complexity Theory
- Robotics
- Geometric Modeling
- Bioinformatics
- Research projects
- Technical leadership
- Faculty mentors
- Scholarship support
- Sponsors
- National Science Foundation
- UMass Lowell
- Lucent Technologies
For additional details and application
information http//morse.uml.edu/iset.html applic
ant screening is underway for Spring, 2005