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Low-Stretch Spanning Trees of Graphs with Bounded Width

Authors Glencora Borradaile, Erin Wolf Chambers, David Eppstein, William Maxwell, Amir Nayyeri

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Author Details

Glencora Borradaile
  • Oregon State University, Corvallis, OR, USA
Erin Wolf Chambers
  • Saint Louis University, MO, USA
David Eppstein
  • University of California, Irvine, CA, USA
William Maxwell
  • Oregon State University, Corvallis, OR, USA
Amir Nayyeri
  • Oregon State University, Corvallis, OR, USA

Funding

This material is based upon work supported by the National Science Foundation under Grant Nos. NSF CCF-1614562, DBI-1759807, CCF-1907612, CCF-1616248, CCF-1617951, CCF-1618301, and CCF-1816442.

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Glencora Borradaile, Erin Wolf Chambers, David Eppstein, William Maxwell, and Amir Nayyeri. Low-Stretch Spanning Trees of Graphs with Bounded Width. In 17th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 162, pp. 15:1-15:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020) https://doi.org/10.4230/LIPIcs.SWAT.2020.15

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.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Graph algorithms
Keywords
  • Treewidth
  • low-stretch spanning tree
  • fundamental cycle basis

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