Approximation Algorithms for NP-Hard Problems.pptx - Approximation Algorithms for NPHard Problems D WINSTON PAUL AP\/IT SKCET Pre-requisites P NP \u2013

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Approximation Algorithms for NP- Hard Problems D. WINSTON PAUL AP/IT SKCET
Pre-requisites P NP NP-Complete NP-Hard
3 NP-completeness Do your best then. !
4 Coping With NP-Hardness Coping With NP-Hardness Brute-force algorithms. Develop clever enumeration strategies. Guaranteed to find optimal solution. No guarantees on running time. Heuristics. Develop intuitive (innovative) algorithms. Guaranteed to run in polynomial time. No guarantees on quality of solution. Approximation algorithms. Guaranteed to run in polynomial time. Guaranteed to find "high quality" solution, say within 1% of optimum. Obstacle: need to prove a solution’s value is close to optimum, without even knowing what optimum value is!
5 Motivation By now we’ve seen many NP-Complete problems. We conjecture none of them has polynomial time algorithm.
6MotivationIs this a dead-end? Should we give up altogether??
Complexity ©D Moshkovitz 7 Motivation Or maybe we can settle for good approximation algorithms?
Approximation Algorithms IS CLOSE ENOUGH GOOD ENOUGH?
Spring 2003 Approximation Algorithmes 10 Performance ratios We are going to find a Near-Optimal solution for a given problem. We assume two hypothesis : Each potential solution has a positive cost.