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Results tagged with computational-complexity
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user 9022
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
sparsity of QR decomposition
Unfortunately you can't. With any orthogonal factorization (e.g. QR, LQ, or SVD) you have the problem that because some of the columns of the orthogonal matrix have to span a particular subspace, and …
- 3,934
22
votes
Can all convex optimization problems be solved in polynomial time using interior-point algor...
As mentioned by another poster, the work of Nesterov and Nemirovski summarized in Interior-Point Polynomial Algorithms in Convex Programming showed that many convex optimization problems (including li …
- 3,934
6
votes
Computational complexity of unconstrained convex optimisation
Some books to start with for background reading would include:
Y. Nesterov, Introductory Lectures on Convex Optimization: A Basic Course, Springer, 2003.
Y. Nesterov and A. Nemirovsky, Interior Poin …
- 3,934
2
votes
Greedy approach to 0-1 Knapsack problem in specific instances
As Frederico has already shown, this isn't enough to make the greedy heuristic immune to counterexamples.
It's worth mentioning that there is a simple dynamic programming algorithm for the knapsack …
- 3,934