## Abstract

This paper studies labeling schemes for flow and connectivity functions. A flow labeling scheme using O(log n · log ω̂ + log^{2} n)-bit labels is presented for general n-vertex graphs with maximum (integral) capacity ω̂. This is shown to be asymptotically optimal. For edge-connectivity, this yields a tight bound of ⊖(log^{2} n) bits. A k-vertex connectivity labeling scheme is then given for general n-vertex graphs using at most 3 log n bits for k = 2, 5 log n bits for k = 3, and 2 ^{k} log n bits for k > 3. Finally, a lower bound of Ω(k log n) is established for k-vertex connectivity on n-vertex graphs, where k is polylogarithmic in n.

Original language | English |
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Pages (from-to) | 23-40 |

Number of pages | 18 |

Journal | SIAM Journal on Computing |

Volume | 34 |

Issue number | 1 |

DOIs | |

State | Published - 2005 |

## Keywords

- Distributed data structures
- Edge-connectivity
- Flow
- Graphs
- Labelmg schemes
- Vertex-connectivity