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Results tagged with computational-complexity
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user 5963
This is a branch that includes: computational complexity theory; complexity classes, NP-completeness and other completeness concepts; oracle analogues of complexity classes; complexity-theoretic computational models; regular languages; context-free languages; Komolgorov Complexity and so on.
9
votes
Accepted
Comparing two numbers given their factorization
According to this paper from 2013 by Etessami, Stewart, and Yannakakis, the time complexity of the [a priori] harder problem where the $p_k$ are not required to be prime is still open. In that paper …
- 8,501
2
votes
Accepted
Does Quadratic Programming get easier when it's described by a diagonal matrix?
The problem is still NP-hard. The proof is by reduction from checking matrix copositivity, which is co-NP-complete. A symmetric matrix $Q$ is said to be copositive if $x^TQx\geq 0$ for all $x\geq 0$ …
- 8,501
16
votes
Independence of P = NP?
There are examples such as the one due to Levin mentioned here which you can write down explicitly, but whose running time is polynomial if and only if P=NP. Thus in some [admittedly rather trivial] …
- 8,501
7
votes
SDP Feasibility
Alex gave a good answer, but I would just like to highlight a subtle problem with your claim about polynomial time solvability of SDPs. This depends on having inner and outer bounding balls to the fe …
- 8,501
5
votes
Computational complexity of low rank SDP
Various NP-hard problems, such as MAX-CUT, can be formulated exactly as SDPs with rank constraints (just google e.g. "max cut sdp"). If you want to enforce such rank constraints anyway, a popular app …
- 8,501
4
votes
Examples of Super-polynomial time algorithmic/induction proofs?
The standard proofs of Sperner's Lemma are the first thing that comes to my mind in this context. They don't have exactly the form you mentioned; in particular they're not really inductive. Nonethel …
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