@article{e8068d9964a94e60b920f862c34e5408,

title = "Using petal-decompositions to build a low stretch spanning tree",

abstract = "We prove that any weighted graph G = (V, E, w) with n points and m edges has a spanning tree T such that \sum \{ u,v\} \in E dT (u,v) = O(m log n log log n). Moreover, such a tree can w(u,v) be found in time O(m log n log log n). Our result is obtained using our new petal-decomposition approach which guarantees that the radius of each cluster in the tree is at most four times the radius of the induced subgraph of the cluster in the original graph.",

keywords = "Distortion, Embedding, Low stretch, Spanning tree",

author = "Ittai Abraham and Ofer Neiman",

note = "Funding Information: The second author was supported in part by ISF grant 1817/17 and BSF grant 2015813. We would like to thank Yair Bartal, Michael Elkin, and Kunal Talwar for helpful discussions, and we thank Arnold Filtser and Benny Kramer for a careful reading of this paper and making useful suggestions. Funding Information: \ast Received by the editors February 9, 2017; accepted for publication (in revised form) January 7, 2019; published electronically March 21, 2019. A preliminary version of this paper appeared in STOC 2012. http://www.siam.org/journals/sicomp/48-2/M111557.html Funding: The second author was supported in part by ISF grant 1817/17 and BSF grant 2015813. \dagger VMware, Palo Alto, CA 94043 (iabraham@vmware.com). \ddagger Department of Computer Science, Ben-Gurion University of the Negev, Beer-Sheva, 84105, Israel (neimano@cs.bgu.ac.il). Publisher Copyright: {\textcopyright} 2019 Society for Industrial and Applied Mathematics",

year = "2019",

month = jan,

day = "1",

doi = "10.1137/17M1115575",

language = "English",

volume = "48",

pages = "227--248",

journal = "SIAM Journal on Computing",

issn = "0097-5397",

publisher = "Society for Industrial and Applied Mathematics Publications",

number = "2",

}