503_lecture1a_S11 - UMass Lowell Computer Science 91.503...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: UMass Lowell Computer Science 91.503 Analysis of Algorithms Prof. Karen Daniels Spring, Spring 2011 Lecture 1 (Part 1) Introduction/Overview I t d ti /O i Tuesday, 1/25/11 Web Page Page Web http://www.cs.uml.edu/~kdaniels/courses/ALG_503_S11.html Nature of the Course Core course: Required for all CS Masters students Required as part of doctoral qualifying structure q p f q fy g Advanced algorithms Builds on undergraduate algorithms 91.404 No programming required "Pencil-and-paper" exercises "Pencil-and Lectures supplemented by: Programs g Real-world examples Real- What's It All About? Algorithm: Algorithm Al ith : steps for the computer to follow to solve a problem recognize structure of some common g problems understand important characteristics of algorithms to solve common problems select appropriate algorithm to solve a problem tailor existing algorithms create new algorithms Some of our goals:(at an advanced level) Some Algorithm Application Areas Robotics Bioinformatics Geographic Information Systems Analyze Design Telecommunications Apply Computer Graphics Voice Recognition Medical Imaging 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? Shortest Path Input: Edge-weighted graph G, with Edgestart vertex s and end vertex t Problem: Find the shortest path from s to t in G Convex Hull C H ll Input: A set S of n points in ddimensional space. Bin Packing g Input: A set of n items with sizes d_1,...,d_n. d_1,...,d_n. A set of m bins with capacity c_1,...,c_m. c_1,...,c_m. Problem: Find the smallest convex polygon containing all the points of S. Problem: How do you store the set of items using the fewest number of bins? SOURCE: SOURCE: Steve Skiena's Algorithm Design Manual (for problem descriptions, see graphics gallery at http://www.cs.sunysb.edu/~algorith) ) Some Typical Problems Transitive Closure Input: A directed graph G=(V,E). G=(V,E). Problem: Construct a graph G'=(V,E') with edge (i,j) in E' iff G (V,E ) E 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 p G' iff (i,j) in E. Edge Coloring Input: A graph G=(V,E). 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? Hamiltonian Cycle y Input: A graph G=(V,E). 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). 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? Tools of the Trade: Core Material Algorithm Design Patterns dynamic programming, linear p g y p g g, programming, g, greedy algorithms, approximation algorithms, randomized algorithms, sweep algorithms, (parallel algorithms) amortized analysis, probabilistic analysis NPNP-completeness, NP-h d l NP-hardness Permutations Number Theory Probability Geometry Advanced Analysis Techniques Theoretical Computer Science principles MATH Logarithms Proofs Calculus Trigonometry Recurrences Linear Algebra Sets Combinations Polynomials P l i l Summations Asymptotic Growth of Functions Prerequisites 91.404 or 94.404. Standard graduate-level prerequisites for g graduatep q math background apply. MATH Combinations Polynomials Summations Permutations Logarithms Calculus Linear Algebra Sets Probability Proofs Recurrences Asymptotic Growth of Functions Geometry Trigonometry Number Theory Textbooks Required: q Introduction to Algorithms by T.H. Corman, C E Leiserson, R L Rivest T H Corman, C.E. Leiserson, R.L. McGraw/Hill and MIT Press 3rd Edition 2009 ISBN 0716710455 see course web site for book s web site containing errata book's see p. 20-22 for pseudocode conventions (different from 2nd edition) 20- Recommended: Garey & Johnson Ordered for UML bookstore Syllabus (current plan) y ( p ) math quiz th i midterm exam final exam Chapter Dependencies Math Review Appendices A, B, C, D Summations, Proof Techniques (e.g. Induction), Sets Induction) Sets, Graphs, Counting & Probability, Matrices Ch 1-13 Foundations Ch 29 Linear Programming Math: Linear Algebra (Appendix D) Ch 33 Computational Geometry Ch 15, 16, 17 15 16 Advanced Design & Analysis Techniques C Ch 22-24,25,26 , 5, 6 Graph Algorithms Ch 34 NP-Completeness Ch 35 Approximation Algorithms Math: Geometry (High School Level) Math: Number Theory Foundations: Automata 3rd Edition Ch 31 Number-Theoretic Algorithms RSA Ch 32 String Matching Important Dates Math Quiz: Tuesday, 2/1 Tuesday, 3/8 y, to be determined In l I class Closed book, no calculators In class Open book, open notes (5/10 is a possibility) Open book, open notes Midterm Exam: Final E am: Exam: Exam am: Grading Homework Midterm Final Exam Instructor's Discretion 30% 30% 35% 5% (open book, notes ) (open book, notes ) Homework HW# Assigned 1 T 1/25 Due T 2/1 Content 91.404 Review (for q ) ( quiz & Chapter 15 ...
View Full Document

Ask a homework question - tutors are online