On miniaturized problems in parameterized complexity theory

Authors:
Yijia Chen;Jörg Flum
Affiliations:
BASICS, Department of Computer Science, Shanghai Jiaotong University, Shanghai, China;Abteilung für Mathematische Logik, Universität Freiburg, Freiburg, Germany
Venue:
Theoretical Computer Science - Parameterized and exact computation
Year:
2006

Citing 6
Cited 2

On the complexity of K-SAT

Journal of Computer and System Sciences - Special issue on the fourteenth annual IEE conference on computational complexity
Which problems have strongly exponential complexity?

Journal of Computer and System Sciences
Fixed-Parameter Tractability, Definability, and Model-Checking

SIAM Journal on Computing
Linear FPT reductions and computational lower bounds

STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Tight Lower Bounds for Certain Parameterized NP-Hard Problems

CCC '04 Proceedings of the 19th IEEE Annual Conference on Computational Complexity
Parameterized Complexity

Parameterized Complexity

Parameterized complexity and subexponential-time computability

The Multivariate Algorithmic Revolution and Beyond
The exponential time hypothesis and the parameterized clique problem

IPEC'12 Proceedings of the 7th international conference on Parameterized and Exact Computation

Quantified Score

Hi-index	0.00

Visualization

Abstract

We introduce a general notion of miniaturization of a problem that comprises the different miniaturizations of concrete problems considered so far. We develop parts of the basic theory of miniaturizations. Using the appropriate logical formalism, we show that the miniaturization of a definable problem in W[t] lies in W[t], too. In particular, the miniaturization of the dominating set problem is in W[2]. Furthermore, we investigate the relation between f(k)ċno(k) time and subexponential time algorithms for the dominating set problem and for the clique problem.