# Questions tagged [polynomial-time]

Use for algorithms, algorithm-analysis and complexity-theory questions that aim for polynomial running time resp. time complexity. Such questions often are are reference-requests or about runtime-analysis or time-complexity.

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### Is there a polynomial time algorithm for this decision problem?

Is there a factor in $M$ that is $>$ $1$, but $<$ $M$ that is NOT a factor of $N$? False Result Example $N$ = 8 $M$ = 16 1, 2, 4, 8, 16 There is no integer that is NOT a factor of $N$ that ...
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### Is co-P recursively enumerable?

P is RE, but is the complement of the class of languages decidable in polynomial time also recursively enumerable? If both are RE then this makes P recursive?
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### Logic of the squared running time in “A Variant of Nondeterministic Acceptance”

I was going through the classic text "Introduction to Automata Theory, Languages, and Computation" by Hofcroft, Ullman, Motwani where I came across the following claim: A Variant of ...
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### Applying Polynomial Time Approximation Scheme (PTAS) on an Algorithm

I am trying to apply PTAS on an algorithm. I think that we apply PTAS on the running time equation of the algorithm. We use the term (1-ϵ) and (1+ ϵ) in the running time of the algorithm but I don’t ...
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### Is longest-path with a specific source and destination impossible in polynomial time?

The problem of finding the longest path in a graph is known to be not be possible in polynomial time, that I am aware of. I am also aware that using DFS or BFS can give the shortest distance between a ...
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### Search reduction to decision

I'm a little stumped on this question (and I don't know the name of it, which is why I've excluded it from the title). I need to describe an algorithm that finds a solution to an NP-Hard problem given ...
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### CRC computation speed vs polynomials features

I tried to find information about how features of a CRC polynomials influence computation speed of implementations. It is obvious that (depending from the CPU architecture the algorithm runs on) ...
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### P is contained in NP ∩ Co-NP?

How should I show that ${\sf P}$ is contained in ${\sf NP} \cap {\sf CoNP}$? I.e., all polynomial time solvable problems and their complements are verifiable in polynomial time.
### is $x^{100000000000}$ a “polynomial time”?
per this post $t = x^2$ means the problem is solvable in "Polynomial" time. per this post in the form $$a_{n}x^{n}+a_{n-1}x^{n-1}+\dotsb +a_{2}x^{2}+a_{1}x+a_{0} { > \boldsymbol{=0}}$$ ...