## Abstract

This article proposes a forbidden-set labeling scheme for the family of unweighted graphs with doubling dimension bounded by α. For an n-vertex graph G in this family, and for any desired precision parameter ϵ > 0, the labeling scheme stores an O(1 + ϵ^{-1})^{2α} log^{2} n-bit label at each vertex. Given the labels of two end-vertices s and t, and the labels of a set F of "forbidden" vertices and/or edges, our scheme can compute, in O(1 + ϵ)^{2α} · |F|^{2} log n time, a 1 + ϵ stretch approximation for the distance between s and t in the graph G \ F. The labeling scheme can be extended into a forbidden-set labeled routing scheme with stretch 1 + ϵ for graphs of bounded doubling dimension.

Original language | English |
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Article number | 22 |

Journal | ACM Transactions on Algorithms |

Volume | 12 |

Issue number | 2 |

DOIs | |

State | Published - Feb 2016 |

Externally published | Yes |

### Bibliographical note

Publisher Copyright:© 2016 ACM.

### Funding

Supported in part by the Israel Science Foundation (grant 894/09), the United States-Israel Binational Science Foundation (grant 2008348), and the Israel Ministry of Science and Technology (infrastructures grant).

Funders | Funder number |
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United States-Israel Binational Science Foundation | 2008348 |

Israel Science Foundation | 894/09 |

Ministry of science and technology, Israel |

## Keywords

- Compact routing
- Distance labeling
- Doubling dimension
- Fault-tolerance
- Forbidden sets