Questions tagged [exp-time-algorithms]

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46
votes
4answers
13k 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
6k 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 ...
14
votes
6answers
455 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 ...
12
votes
2answers
384 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?
13
votes
1answer
872 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
600 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 one ...
8
votes
1answer
433 views

Complexity of validity problem for Monadic First Order Logic?

Monadic First Order Logic is FOL with no function symbols, and predicate symbols restricted to arity 1. For this question, let's say that the = symbol is also forbidden. I want to know the complexity ...