# Time-approximation trade-offs for inapproximable problems

Bonnet, Édouard and Lampis, M and Paschos, V T
(2016)
*Time-approximation trade-offs for inapproximable problems.*
In:
33rd Symposium on Theoretical Aspects of Computer Science, STACS 2016.
Leibniz International Proceedings in Informatics, LIPIcs
(47).
Schloss Dagstuhl Leibniz-Zentrum für Informatik, Dagstuhl, 22:1-22:14.
ISBN 978-3-95977-001-9
10.4230/LIPIcs.STACS.2016.22

Text
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## Abstract

In this paper we focus on problems which do not admit a constant-factor approximation in polynomial time and explore how quickly their approximability improves as the allowed running time is gradually increased from polynomial to (sub-)exponential. We tackle a number of problems: For Min Independent Dominating Set, Max Induced Path, Forest and Tree, for any r(n), a simple, known scheme gives an approximation ratio of r in time roughly rn/r. We show that, for most values of r, if this running time could be significantly improved the ETH would fail. For Max Minimal Vertex Cover we give a nontrivial √r-approximation in time 2n/r. We match this with a similarly tight result. We also give a log r-approximation for Min ATSP in time 2n/r and an r-approximation for Max Grundy Coloring in time rn/r. Furthermore, we show that Min Set Cover exhibits a curious behavior in this superpolynomial setting: for any δ > 0 it admits an mδ-approximation, where m is the number of sets, in just quasi-polynomial time. We observe that if such ratios could be achieved in polynomial time, the ETH or the Projection Games Conjecture would fail. © Édouard Bonnet, Michael Lampis and Vangelis Th. Paschos; licensed under Creative Commons License CC-BY.

Item Type: | Book Section |
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Uncontrolled Keywords: | Polynomial approximation; Quasi-polynomial time; Minimal vertex cover; Independent dominating set; Constant factor approximation; Approximation ratios; Approximability; Polynomials; Economic and social effects; Computational complexity; Approximation algorithms; Algorithms; REDUCTION; Polynomial and subexponential approximation; Inapproximability; COMPLEXITY; ALGORITHM |

Subjects: | Q Science > QA Mathematics and Computer Science > QA75 Electronic computers. Computer science / számítástechnika, számítógéptudomány |

Divisions: | Informatics Laboratory |

SWORD Depositor: | MTMT Injector |

Depositing User: | MTMT Injector |

Date Deposited: | 08 Feb 2017 13:54 |

Last Modified: | 08 Feb 2017 13:54 |

URI: | http://eprints.sztaki.hu/id/eprint/9071 |

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