## Abstract

The paper presents fault-tolerant (FT) labeling schemes for general graphs, as well as, improved FT routing schemes. For a given n-vertex graph G and a bound f on the number of faults, an f-FT connectivity labeling scheme is a distributed data structure that assigns each of the graph edges and vertices a short label, such that given the labels of a vertex pair s and t, and the labels of at most f failing edges F, one can determine if s and t are connected in G \ F. The primary complexity measure is the length of the individual labels. Since their introduction by [Courcelle, Twigg, STACS '07], compact FT labeling schemes have been devised only for a limited collection of graph families. In this work, we fill in this gap by proposing two (independent) FT connectivity labeling schemes for general graphs, with a nearly optimal label length. This serves the basis for providing also FT approximate distance labeling schemes, and ultimately also routing schemes. Our main results for an n-vertex graph and a fault bound f are: There is a randomized FT connectivity labeling scheme with a label length of O(f+log n) bits, hence optimal for f=O(log n). This scheme is based on the notion of cycle space sampling [Pritchard, Thurimella, TALG '11]. There is a randomized FT connectivity labeling scheme with a label length of O(log3 n) bits (independent of the number of faults f). This scheme is based on the notion of linear sketches of [Ahn et al., SODA '12]. For a given stretch parameter k≥ 1, there is a randomized routing scheme that routes a message from s to t in the presence of a set F of faulty edges (unknown to s) over a path of length O(|F|2 k)G \ F (s,t). The routing labels have O (f) bits, the messages have O (f3) bits, and each routing table has only O (f3 n1/k) bits1. The results also hold for weighted graphs with positive polynomial weights. This significantly improves over the state-of-the-art bounds by [Chechik, ICALP '11], providing the first scheme with sub-linear FT labeling and routing schemes for general graphs.

Original language | English |
---|---|

Title of host publication | PODC 2021 - Proceedings of the 2021 ACM Symposium on Principles of Distributed Computing |

Publisher | Association for Computing Machinery |

Pages | 445-455 |

Number of pages | 11 |

ISBN (Electronic) | 9781450385480 |

DOIs | |

State | Published - 21 Jul 2021 |

Externally published | Yes |

Event | 40th ACM SIGACT-SIGOPS Symposium on Principles of Distributed Computing, PODC 2021 - Virtual, Online, Italy Duration: 26 Jul 2021 → 30 Jul 2021 |

### Publication series

Name | Proceedings of the Annual ACM Symposium on Principles of Distributed Computing |
---|

### Conference

Conference | 40th ACM SIGACT-SIGOPS Symposium on Principles of Distributed Computing, PODC 2021 |
---|---|

Country/Territory | Italy |

City | Virtual, Online |

Period | 26/07/21 → 30/07/21 |

### Bibliographical note

Publisher Copyright:© 2021 ACM.

## Keywords

- fault-tolerant labeling schemes
- fault-tolerant routing schemes

## ASJC Scopus subject areas

- Software
- Hardware and Architecture
- Computer Networks and Communications