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Results tagged with algorithms
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user 5963
Informally, an algorithm is a set of explicit instructions used to solve a problem (e.g. Euclid's algorithm for computing the greatest common divisor of two integers). For more specific questions on algorithms, this tag may be used in conjunction with the approximation-algorithms, algorithmic-randomness and algorithmic-topology tags.
4
votes
Accepted
Finding a point that lies in a majority of polytopes
This problem is clearly in NP (guess which polytopes) and becomes NP-complete if we replace $2/3$ with $1/2$ and make it a decision problem, dropping the promise that such a $p$ exists. In particular …
- 8,501
6
votes
Estimate the rank of a vector
Thus I'd guess that this problem is equivalent complexity-wise to #KNAPSACK (which is known to be #P complete but admits various types of approximation algorithms), but there are some details that would …
- 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
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 …
- 8,501
14
votes
Accepted
Effective algorithm to test positivity
If by effective you mean "is this computable", then yes, the computational versions of Tarski-Seidenberg such as cylindrical algebraic decomposition give you a finite algorithm. (I suppose this is ass …
- 8,501