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Results tagged with complexity-theory
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user 4190
Questions related to the (computational) complexity of solving problems
7
votes
1
answer
4k
views
Lower bound for Convex hull
By making use of the fact that sorting $n$ numbers requires
$\Omega(n \log n)$ steps for any optimal algorithm (which uses 'comparison' for sorting), how can I prove that finding the convex-hull of $ …
- 72.9k
14
votes
2
answers
32k
views
Proving DOUBLE-SAT is NP-complete
The well known SAT problem is defined here for reference sake.
The DOUBLE-SAT problem is defined as
$\qquad \mathsf{DOUBLE\text{-}SAT} = \{\langle\phi\rangle \mid \phi \text{ has at least two satis …
- 763
34
votes
Accepted
Proving DOUBLE-SAT is NP-complete
Here is one solution:
Clearly Double-SAT belongs to ${\sf NP}$, since a NTM can decide Double-SAT as follows: On a Boolean input formula $\phi(x_1,\ldots,x_n)$, nondeterministically guess 2 assignmen …
- 763
3
votes
1
answer
1k
views
Complement of HAMPATH
Is the complement of the Hamiltonian Path problem known to be in $\mathsf{NP}$? I could not find explanations saying that it is, but then neither were there any claims saying that it is not in $\maths …
- 12.7k