## Abstract

Vertex Relabeling is a variant of the graph relabeling problem. In this problem, the input is a graph and two vertex labelings, and the question is to determine how close are the labelings. The distance measure is the minimum number of label swaps necessary to transform the graph from one labeling to the other, where a swap is the interchange of the labels of two adjacent nodes. We are interested in the complexity of determining the swap distance. The problem has been recently explored for various restricted classes of graphs, but its complexity in general graphs has not been established. We show that the problem is NP-hard. In addition we consider restricted versions of the problem where a node can only participate in a bounded number of swaps. We show that the problem is NP-hard under these restrictions as well.

Original language | English |
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Title of host publication | Combinatorial Pattern Matching - 26th Annual Symposium, CPM 2015, Proceedings |

Editors | Ugo Vaccaro, Ely Porat, Ferdinando Cicalese |

Publisher | Springer Verlag |

Pages | 1-12 |

Number of pages | 12 |

ISBN (Print) | 9783319199283 |

DOIs | |

State | Published - 2015 |

Event | 26th Annual Symposium on Combinatorial Pattern Matching, CPM 2015 - Ischia Island, Italy Duration: 29 Jun 2015 → 1 Jul 2015 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 9133 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 26th Annual Symposium on Combinatorial Pattern Matching, CPM 2015 |
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Country/Territory | Italy |

City | Ischia Island |

Period | 29/06/15 → 1/07/15 |

### Bibliographical note

Publisher Copyright:© Springer International Publishing Switzerland 2015.

### Funding

B. Porat—Partly supported by a Bar Ilan University President Fellowship. This work is part of Benny Porat’s Ph.D. thesis. A. Amir—Partly supported by ISF grant 571/14.

Funders | Funder number |
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Israel Science Foundation | |

Bar-Ilan University | |

Israel Science Foundation | 571/14 |