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1. Based on our lecture on NP-Complete, can an NP-Complete problem not have a polynomial-time algorithm? Explain your answer. 2. Prove the conjecture that if any problem in NP is not polynomial-time solvable, then no NP-Complete problem is polynomial-time solvable. (You can't use Theorem 1 and 2 directly) 3. After you complete your proof in b), discuss how this conjecture can be used to solve the problem of whether P=NP.

1. Based on our lecture on NP-Complete, can an NP-Complete problem not have a polynomial-time algorithm? Explain your answer. 2. Prove the conjecture that if any problem in NP is not polynomial-time solvable, then no NP-Complete problem is polynomial-time solvable. (You can't use Theorem 1 and 2 directly) 3. After you complete your proof in b), discuss how this conjecture can be used to solve the problem of whether P=NP.

Operations Research : Applications and Algorithms
Operations Research : Applications and Algorithms
4th Edition
ISBN:9780534380588
Author:Wayne L. Winston
Publisher:Wayne L. Winston
Chapter11: Nonlinear Programming
Section11.3: Convex And Concave Functions
Problem 13P
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1. Based on our lecture on NP-Complete, can an NP-Complete problem not have a polynomial-time algorithm? Explain your answer. 2. Prove the conjecture that if any problem in NP is not polynomial-time solvable, then no NP-Complete problem is polynomial-time solvable. (You can't use Theorem 1 and 2 directly) 3. After you complete your proof in b), discuss how this conjecture can be used to solve the problem of whether P=NP.
Transcribed Image Text:1. Based on our lecture on NP-Complete, can an NP-Complete problem not have a polynomial-time algorithm? Explain your answer. 2. Prove the conjecture that if any problem in NP is not polynomial-time solvable, then no NP-Complete problem is polynomial-time solvable. (You can't use Theorem 1 and 2 directly) 3. After you complete your proof in b), discuss how this conjecture can be used to solve the problem of whether P=NP.
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