21_NPCompleteness2 - Wednesday 24/11/10 Dr. Daniel Hughes

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CSC 30155 Wednesday 24/11/10 Dr. Daniel Hughes daniel.hughes@xjtlu.edu.cn
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Today’s Lecture l Recap of NP Completeness (15 mins) l Assignment 4 (5 mins) l Video on NP Completeness (~ 60 mins)
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Conference Notes l You should collect your ID at any of the registration sessions: l Wednesday 5PM-8PM l Thursday 8AM-9AM l Friday 8AM-9AM l Gift packs for volunteers will be distributed in class in Week 13 (when I return from India). l You are welcome to join us for lunch, unfortunately, we don’t have sufficient funds to pay for the banquet too L
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Any Questions?. .
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Supporting Reading l Kleinberg et al., Algorithm Design , Pearson Education, 2005, Chapter 8: NP and Computational Intractability (8.1,8.3 and 8.4). l Cormen et al., Introduction to Algorithms , MIT Press, 2001, Chapter 34: NP- Completeness (34.1, 34.2 and 34.3).
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CSC 30155 Recap of NP Completeness Dr. Daniel Hughes daniel.hughes@xjtlu.edu.cn
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Hard Computational Problems l We have not found efficient algorithms for some computational problems despite numerous attempts. l However, we are also far away from a proof that these problems are hard to solve. l For now, we simply don’t know if an efficient solution exists.
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{0,1} Knapsack – A Hard Problem: l The {0, 1} Knapsack problem can be defined in the following way: l {0, 1} Knapsack (optimization version): l Input: A collection of items {i 1 , i 2 , , i n } where item i j has integer weight w j > 0 and gives integer benefit b j . Also, a maximum weight W (i.e. the most that can be carried in the knapsack). l Goal: Find a subset of the items whose total weight does not exceed W and that maximizes the total benefit ( taking fractional parts of items is not allowed ). l Note: The dynamic programming algorithm for the {0, 1} Knapsack problem runs in time θ (nW) , which is not polynomial in the size of the problem.
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Decision/Optimization Problems: l NP-completeness is formulated in terms of decision problems. A decision problem is a computational problem for which the output is either yes or no. l
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This note was uploaded on 05/22/2011 for the course CSC 30155 taught by Professor Garyli during the Spring '11 term at University of Liverpool.

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21_NPCompleteness2 - Wednesday 24/11/10 Dr. Daniel Hughes

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