License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.SWAT.2020.15
URN: urn:nbn:de:0030-drops-122622
URL: https://drops.dagstuhl.de/opus/volltexte/2020/12262/
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Borradaile, Glencora ; Chambers, Erin Wolf ; Eppstein, David ; Maxwell, William ; Nayyeri, Amir

Low-Stretch Spanning Trees of Graphs with Bounded Width

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LIPIcs-SWAT-2020-15.pdf (0.8 MB)


Abstract

We study the problem of low-stretch spanning trees in graphs of bounded width: bandwidth, cutwidth, and treewidth. We show that any simple connected graph G with a linear arrangement of bandwidth b can be embedded into a distribution T of spanning trees such that the expected stretch of each edge of G is O(b²). Our proof implies a linear time algorithm for sampling from T. Therefore, we have a linear time algorithm that finds a spanning tree of G with average stretch O(b²) with high probability. We also describe a deterministic linear-time algorithm for computing a spanning tree of G with average stretch O(b³). For graphs of cutwidth c, we construct a spanning tree with stretch O(c²) in linear time. Finally, when G has treewidth k we provide a dynamic programming algorithm computing a minimum stretch spanning tree of G that runs in polynomial time with respect to the number of vertices of G.

BibTeX - Entry

@InProceedings{borradaile_et_al:LIPIcs:2020:12262,
  author =	{Glencora Borradaile and Erin Wolf Chambers and David Eppstein and William Maxwell and Amir Nayyeri},
  title =	{{Low-Stretch Spanning Trees of Graphs with Bounded Width}},
  booktitle =	{17th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2020)},
  pages =	{15:1--15:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-150-4},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{162},
  editor =	{Susanne Albers},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/12262},
  URN =		{urn:nbn:de:0030-drops-122622},
  doi =		{10.4230/LIPIcs.SWAT.2020.15},
  annote =	{Keywords: Treewidth, low-stretch spanning tree, fundamental cycle basis}
}

Keywords: Treewidth, low-stretch spanning tree, fundamental cycle basis
Collection: 17th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2020)
Issue Date: 2020
Date of publication: 12.06.2020


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