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A be an NP-complete problem, and if B be an NP-hard problem. If A is polynomial time solvable then is B is polynomial time solvable?

if A be an NP-complete problem, and if B be an NP-hard problem. If A is polynomial time solvable then is B is polynomial time solvable? on the contrary, if A be an NP-complete problem, and B be an NP-...
741 views

How exactly is the process of showing a problem to be NP-Complete a proof by contradiction?

The steps involved in proving that a problem is NP-Complete are fairly straightforward to follow, it's the logic behind why the proof is valid that's really throwing me for a loop. Okay so an easy one:...
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Understanding P, NP with an example decision problem

I was reading the definitions of p vs np in [this post] (What is the definition of P, NP, NP-complete and NP-hard?) and I was wondering about how to classify the example decision problem where you ...
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Is Knapsack-optimization problem NP-hard while Knapsack-search problem NP-complete?

I am learning Computational Complexity. Is Knapsack-optimization problem (find an arrangement to maximize the value) known to be NP-hard, while Knapsack-search problem (find an arrangement so that ...
37 views

What is the difference between NP hard and NP complete?

What is the definition of P, NP, NP-complete and NP-hard? here is a good answer but it really doesn't answer mym question. np-hard-: a problem A is NP hard if for all B$\in$NP, B is polynomial time ...
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Are there problems in NP that do not reduce in polynomial time to any problem in NP?

As the title says: are there problems in $\mathbf{NP}$ that do not reduce in polynomial time to any problem in $\mathbf{NP}$?
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determine Eulerian or Hamiltonian

I am a beginner in graph theory and just found this question in a book after completing few topics and I was wondering how you approach this questions. For eulerian, I can say that the graph has ...
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Proving a problem is NP [duplicate]

I've seen in many textbooks if say we have a problem $Q$, we write a non-deterministic algorithm in polynomial time to solve problem $Q$, and then from that point it results that $Q\in NP$. Why is ...
43 views

Confusion about P versus NP [duplicate]

I'm sure that in my following question my reasoning is extremely simplistic and flawed, but I think if someone answered this it would help me understand what the P vs NP conundrum is. So here is my ...
43 views

What are the differences between NP-Complete and NP-Hard? [duplicate]

What are the differences between NP, NP-Complete and NP-Hard? I am aware of many resources all over the web. I'd like to read your explanations, and the reason is they might be different from what's ...
238 views

How to prove NP-hardness from scratch?

I am working on a problem of whose complexity is unknown. By the nature of the problem, I cannot use long edges as I please, so 3SAT and variants are almost impossible to use. Finally, I have decided ...
545 views

P/NP - Polynomial Reduction vs Certificate

I am learning about the P/NP problem right now, and I don't understand when to use polynomial reduction and when to use a certificate. How I understand polynomial reduction is that you can use it to ...
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What's the purpose of the non-deterministic Turing machine?

(*) Acronyms NTDM := non-deterministic Turing machine. TM := deterministic Turing machine. (*) Consider the following idea The NTDM is able to follow, in parallel, all paths of the tree of the ...
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Pseudo-Proof of Constrained Sudoku is co-np

The definition of CO-NP A decision problem X is a member of co-NP if and only if its complement X is in the complexity class NP. In other words, co-NP is the class of problems for which there ...