Lower-stretch spanning trees

Michael Elkin, Daniel A. Spielman, Yuval Emek, Shang Hua Teng

Research output: Contribution to journalConference articlepeer-review

66 Scopus citations


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 languageEnglish
Pages (from-to)494-503
Number of pages10
JournalProceedings of the Annual ACM Symposium on Theory of Computing
StatePublished - 1 Dec 2005
Event13th Color Imaging Conference: Color Science, Systems, Technologies, and Applications - Scottsdale, AZ, United States
Duration: 7 Nov 200511 Nov 2005


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

ASJC Scopus subject areas

  • Software


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