lecture_24

# lecture_24 - Introduction to Algorithms 6.046J/18.401J...

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Introduction to Algorithms 6.046J/18.401J Lecture 24 Prof. Piotr Indyk

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Dealing with Hard Problems What to do if: – Divide and conquer – Dynamic programming –Greedy – Linear Programming/Network Flows –… does not give a polynomial time algorithm? © Piotr Indyk Introduction to Algorithms December 8, 2004 L24.2
Dealing with Hard Problems Solution I: Ignore the problem – Can’t do it ! There are thousands of problems for which we do not know polynomial time algorithms – For example: • Traveling Salesman Problem (TSP) • Set Cover © Piotr Indyk Introduction to Algorithms December 8, 2004 L24.3

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Traveling Salesman Problem Traveling Salesman Problem (TSP) – Input: undirected graph with lengths on edges – Output: shortest cycle that visits each vertex exactly once Best known algorithm: O(n 2 n ) time. © Piotr Indyk Introduction to Algorithms December 8, 2004 L24.4
Bank robbery problem: Set Cover: X={plan, shoot, safe, – Input: subsets S 1 …S n of X , drive, scary} i S i = X , |X|=m Sets: – Output: C {1…n} , such –S Joe ={plan, safe} that i C S i = X , and |C| –S Jim ={shoot, scary, minimal drive} Best known algorithm:

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lecture_24 - Introduction to Algorithms 6.046J/18.401J...

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