### Abstract

Given a graph G on n nodes the authors say that a graph T on n + k nodes is a k-fault tolerant version of G, if one can embed G in any n node induced subgraph of T. Thus T can sustain k faults and still emulate G without any performance degradation. They show that for a wide range of values of n, k and d, for any graph on n nodes with maximum degree d there is a k-fault tolerant graph with maximum degree O(kd). They provide lower bounds as well: there are graphs G with maximum degree d such that any k-fault tolerant version of them has maximum degree at least Omega (d square root k).

Original language | English |
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Title of host publication | Proceedings - 33rd Annual Symposium on Foundations of Computer Science, FOCS 1992 |

Publisher | IEEE Computer Society |

Pages | 693-702 |

Number of pages | 10 |

ISBN (Electronic) | 0818629002 |

DOIs | |

Publication status | Published - Jan 1 1992 |

Event | 33rd Annual Symposium on Foundations of Computer Science, FOCS 1992 - Pittsburgh, United States Duration: Oct 24 1992 → Oct 27 1992 |

### Publication series

Name | Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS |
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Volume | 1992-October |

ISSN (Print) | 0272-5428 |

### Conference

Conference | 33rd Annual Symposium on Foundations of Computer Science, FOCS 1992 |
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Country | United States |

City | Pittsburgh |

Period | 10/24/92 → 10/27/92 |

### Fingerprint

### ASJC Scopus subject areas

- Computer Science(all)

### Cite this

*Proceedings - 33rd Annual Symposium on Foundations of Computer Science, FOCS 1992*(pp. 693-702). [267781] (Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS; Vol. 1992-October). IEEE Computer Society. https://doi.org/10.1109/SFCS.1992.267781

**Fault tolerant graphs, perfect hash functions and disjoint paths.** / Ajtai, M.; Alon, N.; Bruck, J.; Cypher, R.; Ho, C. T.; Naor, M.; Szemerédi, E.

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

*Proceedings - 33rd Annual Symposium on Foundations of Computer Science, FOCS 1992.*, 267781, Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS, vol. 1992-October, IEEE Computer Society, pp. 693-702, 33rd Annual Symposium on Foundations of Computer Science, FOCS 1992, Pittsburgh, United States, 10/24/92. https://doi.org/10.1109/SFCS.1992.267781

}

TY - GEN

T1 - Fault tolerant graphs, perfect hash functions and disjoint paths

AU - Ajtai, M.

AU - Alon, N.

AU - Bruck, J.

AU - Cypher, R.

AU - Ho, C. T.

AU - Naor, M.

AU - Szemerédi, E.

PY - 1992/1/1

Y1 - 1992/1/1

N2 - Given a graph G on n nodes the authors say that a graph T on n + k nodes is a k-fault tolerant version of G, if one can embed G in any n node induced subgraph of T. Thus T can sustain k faults and still emulate G without any performance degradation. They show that for a wide range of values of n, k and d, for any graph on n nodes with maximum degree d there is a k-fault tolerant graph with maximum degree O(kd). They provide lower bounds as well: there are graphs G with maximum degree d such that any k-fault tolerant version of them has maximum degree at least Omega (d square root k).

AB - Given a graph G on n nodes the authors say that a graph T on n + k nodes is a k-fault tolerant version of G, if one can embed G in any n node induced subgraph of T. Thus T can sustain k faults and still emulate G without any performance degradation. They show that for a wide range of values of n, k and d, for any graph on n nodes with maximum degree d there is a k-fault tolerant graph with maximum degree O(kd). They provide lower bounds as well: there are graphs G with maximum degree d such that any k-fault tolerant version of them has maximum degree at least Omega (d square root k).

UR - http://www.scopus.com/inward/record.url?scp=79952398316&partnerID=8YFLogxK

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U2 - 10.1109/SFCS.1992.267781

DO - 10.1109/SFCS.1992.267781

M3 - Conference contribution

T3 - Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS

SP - 693

EP - 702

BT - Proceedings - 33rd Annual Symposium on Foundations of Computer Science, FOCS 1992

PB - IEEE Computer Society

ER -