Stack Exchange Network

Stack Exchange network consists of 174 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

Questions tagged [np-complete]

The tag has no usage guidance.

18
votes
1answer
422 views

Natural candidate against the Isomorphism Conjecture?

The famous Isomorphism Conjecture of Berman and Hartmanis says that all $NP$-complete languages are polynomial time isomorphic (p-isomorphic) to each other. The key significance of the conjecture is ...
14
votes
2answers
342 views

Poly time superset of NP complete language with infinitely many strings excluded from it

For any arbitrary NP complete language is there always a polytime superset the complement of which is also infinite? A trivial version which does not stipulate the superset to have infinite ...
1
vote
1answer
303 views

in SAT resolution proofs, are all DAGs possible? [closed]

these are some probably very hard but possibly significant and deep questions related to an unusual but intriguing possible "recursive" construction/formulation in SAT, with some important "structure" ...
35
votes
1answer
994 views

NP-Completeness of the decision problem for the generalized 15-puzzle

I am interested in the natural generalization of the famous 15-puzzle, where you have to slide blocks until you have sorted all given numbers (usally there is a gap of 1 block). Now the ...
20
votes
1answer
674 views

“Almost easy” NP-complete problems

Let us say that a language $L$ is P-density-close if there is a polynomial time algorithm that correctly decides $L$ on almost all inputs. In other words, there is an $A\in$ P, such that $L\Delta A$...
7
votes
1answer
269 views

Is every coNP-complete language P-isomorphic to an P-immune coNP-complete language? OR Is there a P-immune coNP-complete language?

A set is $\mathsf{P}$-immune iff it has no non-trivial $\mathsf{P}$ subset. Is every $\mathsf{coNP}$-complete language $\mathsf{P}$-isomorphic to an $\mathsf{P}$-immune $\mathsf{coNP}$-complete ...
5
votes
2answers
710 views

Isn't it trivial to represent any classical Physics problem in a Spin-Glass format which is NP-Complete?

In the late 80's there were several efforts to use Spin-Glass models to formulate other computational problems such as: Protein Folding and Neural Networks. Wouldn't it be straight forward to reduce ...
8
votes
1answer
293 views

Can a natural graph problem be universally hard?

Is there a natural $\mathsf{NP}$-complete graph problem, which remains $\mathsf{NP}$-complete even when it is restricted to any polynomial-time recognizable graph class? To avoid degenerated cases, ...
-2
votes
2answers
585 views

Where are NP-complete problems if P=NP [closed]

Where are exactly NP-complete problems if P=NP? They will be definitely in P, but will they be P-complete?
4
votes
1answer
575 views

Is approximating Exact Set Cover NP-hard for constant approximation factor? ETH hard?

It is known that Exact Set Cover is an NP-hard problem (Reduction from 3-SAT and 3-Coloring). Also, my minor analysis one can realize that this problem is also ETH-hard, i.e. this cannot be solved in ...
3
votes
1answer
445 views

Easier and Harder instances of NP-complete problems?

Following previous questions here and here around $NP$-complete problems (and P vs NP). Are there "easier" or "harder" (sets of) instances of an $NP$-complete problem? If yes (which i assume), how a ...
0
votes
1answer
153 views

Any result connecting an NP-complete problem with slight super-polynomial time?

Helo everybody, is there any result or research that connects some $NP$-complete problem with only slightly super-polynomial (strongly sub-exponential) time? This would not necessarily involve ...