Lec2_Approx

Lec2_Approx - COT 6936: Topics in Algorithms! Giri...

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COT 6936: Topics in Algorithms Giri Narasimhan ECS 254A / EC 2443; Phone: x3748 giri@cs.fiu.edu http://www.cs.fiu.edu/~giri/teach/COT6936_S12.html https://online.cis.fiu.edu/portal/course/view.php?id= XXX
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Expectations • Attend class • Do required reading before class • Participate in class discussions • Team work; discussion groups • Solve practical research problems • Make a presentation; write a report – need a research component; may implement • Write research paper • No cell phones, SMS, or email during class 1/23/12 COT 6936 2
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1/23/12 COT 6936 3 Evaluation • Exam (1) 20% • Quizzes 5% • Homework Assignments 15% • Semester Project 40% • Class Participation 20%
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• Milestones: – By Jan 23: Meet with me and discuss project – By Jan 30: Send me email with project team information and topic – Feb 20 : Short presentation giving intro to project, problem definition, notation, and background – March 5 : Take-home Exam – April 16, 23 : Final presentation of project – April 24 : Written report on project 1/23/12 COT 6936 4
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Homework #1 • Achieving diversity in heights: – Largest empty range problem – Smallest empty range problem – Which is harder and why? • Binary Counter – How many bits were changed when a binary counter is incremented from 0 to N? • Drunken Sailors problem – How many sailors will sleep in their own cabins? • ACM Programming Contest Problems 1/23/12 COT 6936 5
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Reading • Read Background – Algorithms & Discrete Math Fundamentals • Cormen, et al., Chapters 1-16, 22-25 – NP-Completeness • Cormen et al., Chapter 34 • Appendix (p187-288) form Garey & Johnson • Next Class – Approximation Algorithms • Cormen et al., Chapter 35 • Kleinberg, Tardos, Chapter 11 • Books by Vazirani and Hochbaum/Shmoys 1/23/12 COT 6936 6
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1/23/12 COT 6936 7 What are NP-Complete problems? • These are the hardest problems in NP . • A problem p is if – there is a polynomial-time reduction from every problem in NP to p . – p • How to prove that a problem is ? Cook s Theorem : [1972] –The SAT problem is . Steve Cook, Richard Karp, Leonid Levin
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1/23/12 COT 6936 8 The SAT Problem: an example • Consider the boolean expression: C = (a ¬ b c) ( ¬ a d ¬ e) (a ¬ d ¬ c) • Is C satisfiable? [ Does there exist a True/False assignments to the boolean variables a, b, c, d, e , such that C is True? ] • If there are n boolean variables, then there are 2 n different truth value assignments. • However, a solution can be quickly verified!
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1/23/12 COT 6936 9 The SAT (Satisfability) Problem Input : Boolean expression C in Conjunctive normal form (CNF) in n variables and m clauses. Question
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Lec2_Approx - COT 6936: Topics in Algorithms! Giri...

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