Lower-Stretch Spanning Trees

@inproceedings{Elkin2005LowerStretchST,
  title={Lower-Stretch Spanning Trees},
  author={Michael Elkin and Daniel A. Spielman and Shang-Hua Teng},
  booktitle={STOC},
  year={2005}
}
We show that every weighted connected graph <i>G</i> contains as a subgraph a spanning tree into which the edges of <i>G</i> can be embedded with average stretch <i>O</i> (log<sup>2</sup> <i>n</i> log log <i>n</i>). Moreover, we show that this tree can be constructed in time <i>O</i> (<i>m</i> log<sup>2</sup><i>n</i>) in general, and in time <i>O</i> (<i>m</i>log <i>n</i>) if the input graph is unweighted. The main ingredient in our construction is a novel graph decomposition technique.Our new… CONTINUE READING