## Abstract

We prove that every unweighted series-parallel graph can be probabilistically embedded into its spanning trees with logarithmic distortion. This is tight due to an Ω(log n) lower bound established by Gupta, Newman, Rabinovich, and Sinclair on the distortion required to probabilistically embed the n-vertex diamond graph into a collection of dominating trees. Our upper bound is gained by presenting a polynomial time probabilistic algorithm that constructs spanning trees with low expected stretch. This probabilistic algorithm can be derandomized to yield a deterministic polynomial time algorithm for constructing a spanning tree of a given (unweighted) series-parallel graph G, whose communication cost is at most O(log n) times larger than that of G.

Original language | English |
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Pages (from-to) | 1827-1841 |

Number of pages | 15 |

Journal | SIAM Journal on Discrete Mathematics |

Volume | 23 |

Issue number | 4 |

DOIs | |

State | Published - 2009 |

Externally published | Yes |

## Keywords

- Probabilistic embedding
- Series-parallel graphs
- Spanning trees