<p>Yes, just think how you would use a SAT solver to solve the independent set problem.</p>
<p>If you have one variable per node, it should be clear how to write constraints that guarantee that variables that are true indeed form an independent set. I think the only non-trivial part is counting: how to make sure that your independent set is sufficiently large. For that you can use BDD-based techniques; see e.g. Section 5.3 of <a href="https://doi.org/10.3233/SAT190014" rel="nofollow noreferrer">this paper</a>.</p>

CC BY-SA 4.0
2020-09-15T19:42:18.833Z
Any chance you could update the broken link / add citation info? I can't access it and can't tell what it's supposed to be pointing to. Thanks in advance!
Joshua Grochow
CC BY-SA 4.0
2020-09-15T20:39:53.043Z
@JoshuaGrochow Fixed the link!
Jukka Suomela
CC BY-SA 4.0
2020-09-16T00:56:30.517Z
For some of these problems it is easier to reduce to Circuit SAT since one is presumably used to the  idea of implementing arithmetic naturally via circuits and  gates. And then use a Karp reduction from Circuit SAT to SAT. This is assuming that one wants to "see" a somewhat natural reduction  rather than  use a SAT solver etc.
Chandra Chekuri
CC BY-SA 4.0
2010-08-26T07:43:17.243Z
2020-09-15T20:39:34.547Z
2020-09-15T20:39:34.547Z
Jukka Suomela
<p>Is there a natural <a href="http://en.wikipedia.org/wiki/Polynomial-time_reduction" rel="nofollow">Karp reduction</a> from Independent Set to SAT ? That is, a reduction that does not rely on the Turing machine (as the case in proof of Cook's theorem) but the combinatorial structure.</p>

<cc.complexity-theory><reductions>
Is there any natural Karp reduction from Independent Set problem to SAT?
Regularity
# Is there any natural Karp reduction from Independent Set problem to SAT?

(Asked by: username_0 on 2010-08-26)

Is there a natural [Karp reduction](http://en.wikipedia.org/wiki/Polynomial-time_reduction) from Independent Set to SAT ? That is, a reduction that does not rely on the Turing machine (as the case in proof of Cook's theorem) but the combinatorial structure.

**Tags:** cc.complexity-theory, reductions


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## 1 answers

### Answer by username_1 on 2010-08-26. Score: 12 | Accepted answer

Yes, just think how you would use a SAT solver to solve the independent set problem.

If you have one variable per node, it should be clear how to write constraints that guarantee that variables that are true indeed form an independent set. I think the only non-trivial part is counting: how to make sure that your independent set is sufficiently large. For that you can use BDD-based techniques; see e.g. Section 5.3 of [this paper](https://doi.org/10.3233/SAT190014).

> **Comments:**
> **username_2**: Any chance you could update the broken link / add citation info? I can't access it and can't tell what it's supposed to be pointing to. Thanks in advance!  
> **username_1**: @JoshuaGrochow Fixed the link!  
> **username_3**: For some of these problems it is easier to reduce to Circuit SAT since one is presumably used to the  idea of implementing arithmetic naturally via circuits and  gates. And then use a Karp reduction from Circuit SAT to SAT. This is assuming that one wants to "see" a somewhat natural reduction  rather than  use a SAT solver etc.  

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