Lecture 1 (Part 1) Introduction/Overview

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1 UMass Lowell Computer Science Analysis of Algorithms Prof. Karen Daniels Fall, 2013 Lecture 1 (Part 1) Introduction/Overview Monday, 9/9/13

2 Web Page Web Page

3 Nature of the Course Core course: Required for all CS Masters students Part of doctoral qualifying structure 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 Bioinformatics Geographic Information Systems Robotics Design Analyze Telecommunications Computer Apply Graphics Medical Imaging Voice Recognition

6 (for problem descriptions, see graphics gallery at Some Typical Problems 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? 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. 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? SOURCE: Steve Skiena s Algorithm Design Manual

7 Some 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. Hamiltonian Cycle Input: A graph G=(V,E). Problem: Find an ordering of the vertices such that each vertex is visited exactly 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? 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?

8 Tools of the Trade: Core Material Algorithm Design Patterns dynamic programming, greedy algorithms, approximation algorithms, randomized algorithms, sweep algorithms, multithreaded algorithms Advanced Analysis Techniques amortized analysis, probabilistic analysis Theoretical Computer Science principles NP-completeness, NP-hardness Combinations Polynomials Summations Permutations Number Theory MATH Probability Logarithms Proofs Calculus Linear Algebra Sets Trigonometry Recurrences

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

10 Textbooks Required: Introduction to Algorithms by T.H. Corman, C.E. Leiserson, R.L. Rivest McGraw/Hill and MIT Press 2009 ISBN see course web site for book s web site containing errata see p for pseudocode conventions (different from 2 nd edition) Recommended: Garey & Johnson Ordered for UML bookstore 3 rd Edition

11 Syllabus (current plan) quiz midterm exam final exam

12 Chapter Dependencies Math Review Appendices A, B, C, D Summations, Proof Techniques (e.g. Induction), Sets, Graphs, Counting & Probability, Matrices Ch 15, 16, 17 Advanced Design & Analysis Techniques Ch 22-24,25,26 Graph Algorithms Ch 34 NP-Completeness Ch 35 Approximation Algorithms Ch 1-13 Foundations Math: Linear Algebra (Appendix D) Math: Geometry (High School Level) Foundations: Automata Ch 33 Computational Geometry Ch 32 String Matching Ch 27 Multithreaded Algorithms 3 rd Edition

13 Important Dates Math (& ) Quiz Monday, 9/16 In class Closed book Midterm Exam: Wednesday, 10/16 (Monday schedule) In class Open book, open notes, no electronic devices Final Exam: to be determined Open book, open notes

14 Grading Homework 30% Math Quiz 5% Midterm 30% (open book, notes ) Final Exam 33% (open book, notes ) Instructor s Discretion 2%

15 Homework HW# Assigned Due Content 1 M 9/9 M 9/16 Chapter 15 Attach honor statement (see ethics policy) Algorithm description: Pseudocode (conventions from p ) Correctness justification Mechanical As-advertised Complexity: typically upper bound on worstcase asymptotic time

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