Approximation Algorithms for NP-Hard ProblemsD. WINSTON PAULAP/ITSKCET
3NP-completenessDo your best then.!
4Coping With NP-HardnessCoping With NP-HardnessBrute-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!
5MotivationBy 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??