@inproceedings{802911f28932402cbd4847ca221852e0,

title = "Lower-Stretch Spanning Trees",

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.",

keywords = "Low-distortion embeddings, Low-stretch spanning trees, Probabilistic tree metrics",

author = "Michael Elkin and Spielman, {Daniel A.} and Yuval Emek and Teng, {Shang Hua}",

year = "2005",

month = may,

doi = "10.1145/1060590.1060665",

language = "אנגלית",

isbn = "1581139608",

series = "Proceedings of the Annual ACM Symposium on Theory of Computing",

publisher = "Association for Computing Machinery",

pages = "494--503",

booktitle = "STOC '05: Proceedings of the 37th Annual ACM Symposium on Theory of Computing",

note = "13th Color Imaging Conference: Color Science, Systems, Technologies, and Applications ; Conference date: 07-11-2005 Through 11-11-2005",

}