### Abstract

A pseudoforest is a graph where each connected component contains at most one cycle, or alternatively, a graph that can be turned into a forest by removing at most one edge from each connected component. In this paper, we show that the following problem can be solved in O(3^{k}nk^{O}(1)) time: given a graph G and an integer k, can we delete at most k vertices from G such that we obtain a pseudoforest? The result improves upon an earlier result by Philip et al. [MFCS 2015] who gave a (nonlinear) 7.56^{k}n^{O(1)}-time algorithm both in the exponential factor depending on k as well as in the polynomial factor depending on n.

Original language | English |
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Title of host publication | 11th International Symposium on Parameterized and Exact Computation, IPEC 2016 |

Editors | Jiong Guo, Danny Hermelin |

Publisher | Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing |

ISBN (Electronic) | 9783959770231 |

DOIs | |

Publication status | Published - Feb 1 2017 |

Event | 11th International Symposium on Parameterized and Exact Computation, IPEC 2016 - Aarhus, Denmark Duration: Aug 24 2016 → Aug 26 2016 |

### Publication series

Name | Leibniz International Proceedings in Informatics, LIPIcs |
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Volume | 63 |

ISSN (Print) | 1868-8969 |

### Other

Other | 11th International Symposium on Parameterized and Exact Computation, IPEC 2016 |
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Country | Denmark |

City | Aarhus |

Period | 8/24/16 → 8/26/16 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Software

### Cite this

*11th International Symposium on Parameterized and Exact Computation, IPEC 2016*[7] (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 63). Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. https://doi.org/10.4230/LIPIcs.IPEC.2016.7

**A faster parameterized algorithm for pseudoforest deletion.** / Bodlaender, Hans L.; Ono, Hirotaka; Otachi, Yota.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*11th International Symposium on Parameterized and Exact Computation, IPEC 2016.*, 7, Leibniz International Proceedings in Informatics, LIPIcs, vol. 63, Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 11th International Symposium on Parameterized and Exact Computation, IPEC 2016, Aarhus, Denmark, 8/24/16. https://doi.org/10.4230/LIPIcs.IPEC.2016.7

}

TY - GEN

T1 - A faster parameterized algorithm for pseudoforest deletion

AU - Bodlaender, Hans L.

AU - Ono, Hirotaka

AU - Otachi, Yota

PY - 2017/2/1

Y1 - 2017/2/1

N2 - A pseudoforest is a graph where each connected component contains at most one cycle, or alternatively, a graph that can be turned into a forest by removing at most one edge from each connected component. In this paper, we show that the following problem can be solved in O(3knkO(1)) time: given a graph G and an integer k, can we delete at most k vertices from G such that we obtain a pseudoforest? The result improves upon an earlier result by Philip et al. [MFCS 2015] who gave a (nonlinear) 7.56knO(1)-time algorithm both in the exponential factor depending on k as well as in the polynomial factor depending on n.

AB - A pseudoforest is a graph where each connected component contains at most one cycle, or alternatively, a graph that can be turned into a forest by removing at most one edge from each connected component. In this paper, we show that the following problem can be solved in O(3knkO(1)) time: given a graph G and an integer k, can we delete at most k vertices from G such that we obtain a pseudoforest? The result improves upon an earlier result by Philip et al. [MFCS 2015] who gave a (nonlinear) 7.56knO(1)-time algorithm both in the exponential factor depending on k as well as in the polynomial factor depending on n.

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U2 - 10.4230/LIPIcs.IPEC.2016.7

DO - 10.4230/LIPIcs.IPEC.2016.7

M3 - Conference contribution

AN - SCOPUS:85014711805

T3 - Leibniz International Proceedings in Informatics, LIPIcs

BT - 11th International Symposium on Parameterized and Exact Computation, IPEC 2016

A2 - Guo, Jiong

A2 - Hermelin, Danny

PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing

ER -