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In terms of worst-case asymptotic runtime, which NP-complete problem has the fastest-known (exact) algorithm and what is the algorithm? Is there something known that is faster than $O(n^2*2^n)$?

Raphael
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Wuschelbeutel Kartoffelhuhn
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1 Answers1

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Vertex Cover has an algorithm running in time $1.2738^k + nk$, and is thus faster than $2^n n^2$, even with $k=n$. You can check out Table of FPT races for a short list of FPT running times of different problems. Here, $n$ is the number of vertices and $k$ is the solution size.

Also, the question Are there subexponential-time algorithms for NP-complete problems? addresses similar questions.

Community
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Ainsley H.
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