## Abstract

We show that every weighted connected graph G contains as a subgraph a spanning tree into which the edges of G can be embedded with average stretch O(log ^{2} n log log n). Moreover, we show that this tree can be constructed in time O(m log ^{2} n) in general, and in time O(m log n) if the input graph is unweighted. The main ingredient in our construction is a novel graph decomposition technique. Our new algorithm can be immediately used to improve the running time of the recent solver for symmetric diagonally dominant linear systems of Spielman and Teng from m2 ^{(O(√log n log log n))} to m log ^{o(1)} n, and to O(n log ^{2} n log log n) when the system is planar. Our result can also be used to improve several earlier approximation algorithms that use low-stretch spanning trees.

Original language | English |
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Pages (from-to) | 494-503 |

Number of pages | 10 |

Journal | Proceedings of the Annual ACM Symposium on Theory of Computing |

DOIs | |

State | Published - 1 Dec 2005 |

Event | 13th Color Imaging Conference: Color Science, Systems, Technologies, and Applications - Scottsdale, AZ, United States Duration: 7 Nov 2005 → 11 Nov 2005 |

## Keywords

- Low-distortion embeddings
- Low-stretch spanning trees
- Probabilistic tree metrics

## ASJC Scopus subject areas

- Software