# 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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### 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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### Subset Sum With Interval Target

Define the subset sum with interval target problem (SSITP) as follows: SSITP Input: A multiset $S = \{a_1, …, a_p\}$ of positive integers $a_i$ such that $\sum_{a_i \in S} a_i = T$. SSITP Output: ...
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### Does an FPTAS exist for the multiple subset sum problem when m is fixed and c is not a variable?

From Wikipedia Multiple subset sum: The multiple subset sum problem (MSSP) is a generalization of the subset sum problem (SSP): given a multiset $S$ of $n$ integers, and an integer $m$, the goal is to ...
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### Pseudo-polynomial Algorithms

Reading wikipedia I found that they give this example Consider the problem of testing whether a number n is prime, by naively checking whether no number in $\{2,3,\dotsc ,\sqrt {n}\}$ divides $n$ ...
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### Differences between Polynomial and fully polynomial time approximation scheme

I have a confusion on understanding the relation between: The input n ,The relative error and The running time of the program In both PTAS and FPTAS. In "The running time of PTAS must be ...
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### Polynomial and fully polynomial time approximation scheme

How to notice the type of algorithm whether it is polynomial or fully polynomial time approximation from the resulting running time ( execution time) of the program? Is there any other way to decide?
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### Is there a difference between extremely slow growing functions and constants with respect to computable functions?

So let's say we have the function $f(n)$ that gives $k$ such that $k$ is the smallest number that gives a busy beaver function $B$ value from input $k$ that is greater than $n$. Or more succinctly the ...