Questions tagged [exp-time-algorithms]

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44
votes
4answers
12k views

Approximation algorithms for Metric TSP

It is known that metric TSP can be approximated within $1.5$ and cannot be approximated better than $123\over 122$ in polynomial time. Is anything known about finding approximation solutions in ...
9
votes
2answers
5k views

Time complexity of Held-Karp algorithm for TSP

When I looked through "A Dynamic Programming Approach to Sequencing Problems" by Michael Held and Richard M. Karp, I came up with the following question: why the complexity of their algorithm for TSP ...
12
votes
2answers
347 views

$\overline{SAT} \in NTIME(subexp)$?

Is it possible that $\overline{SAT} \in NTIME(\exp(n^{0.9}))$ ? Are there interesting consequences of such containment? Would it contradict the Exponential Time Hypothesis?
8
votes
3answers
260 views

Problems with Unknown Single Exponential Time Agorithms

I'm looking for examples of problems for which it is easy to get algorithms running in time $2^{O(n\log n)}$, or $2^{O(n^c)}$ for some $c>1$ but for which it is not known whether there is an ...
13
votes
1answer
792 views

Exact algorithms for non-convex quadratic programming

This question is about quadratic programming problems with box constraints (box-QP), i.e., optimisation problems of the form minimise $f(\mathbf{x}) = \mathbf{x}^T A \mathbf{x} + \mathbf{c}^T \mathbf{...
10
votes
2answers
575 views

Exact exponential-time algorithms for 0-1 programming

Are there known algorithms for the following problem that beat the naive algorithm? Input: A system $Ax \le b$ of $m$ linear inequalities. Output: A feasible solution $x^*\in \{0,1 \}^n$ if ...