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# note12 - Outline 1 2 3 4 5 6 7 8 How to Deal with N PC...

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Outline 1 How to Deal with NPC Problems 2 Approximation Algorithms 3 Heuristic Algorithms 4 Approximation Algorithms: Minimum Vertex Cover (MVC) 5 Traveling Salesman Problem (TSP) 6 TSP: Approximation Algorithm 7 TSP: Christofides Algorithm 8 Polynomial Time Approximation Scheme c Xin He (University at Buffalo) CSE 431/531 Algorithm Analysis and Design 1 / 44

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Approximation Algorithms We have a NPC problem Q . c Xin He (University at Buffalo) CSE 431/531 Algorithm Analysis and Design 2 / 44
Approximation Algorithms We have a NPC problem Q . Then it is extremely unlikely Q can be solved in polynomial time. What to do? Just give up? c Xin He (University at Buffalo) CSE 431/531 Algorithm Analysis and Design 2 / 44

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Approximation Algorithms We have a NPC problem Q . Then it is extremely unlikely Q can be solved in polynomial time. What to do? Just give up? Many NPC problems are natural problems with important applications. We cannot afford to just give up! c Xin He (University at Buffalo) CSE 431/531 Algorithm Analysis and Design 2 / 44
Approximation Algorithms We have a NPC problem Q . Then it is extremely unlikely Q can be solved in polynomial time. What to do? Just give up? Many NPC problems are natural problems with important applications. We cannot afford to just give up! Many NPC problems are hard to solve if we insist on absolute optimal solution . c Xin He (University at Buffalo) CSE 431/531 Algorithm Analysis and Design 2 / 44

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Approximation Algorithms We have a NPC problem Q . Then it is extremely unlikely Q can be solved in polynomial time. What to do? Just give up? Many NPC problems are natural problems with important applications. We cannot afford to just give up! Many NPC problems are hard to solve if we insist on absolute optimal solution . But if we settle for nearly optimal solutions (for example, within 50 % of optimal), it might be possible to solve Q . c Xin He (University at Buffalo) CSE 431/531 Algorithm Analysis and Design 2 / 44
Approximation Algorithms We have a NPC problem Q . Then it is extremely unlikely Q can be solved in polynomial time. What to do? Just give up? Many NPC problems are natural problems with important applications. We cannot afford to just give up! Many NPC problems are hard to solve if we insist on absolute optimal solution . But if we settle for nearly optimal solutions (for example, within 50 % of optimal), it might be possible to solve Q . In many applications, a nearly optimal solution might be good enough. c Xin He (University at Buffalo) CSE 431/531 Algorithm Analysis and Design 2 / 44

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Approximation Algorithms We have a NPC problem Q . Then it is extremely unlikely Q can be solved in polynomial time. What to do? Just give up? Many NPC problems are natural problems with important applications. We cannot afford to just give up! Many NPC problems are hard to solve if we insist on absolute optimal solution .
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note12 - Outline 1 2 3 4 5 6 7 8 How to Deal with N PC...

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