eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2020-06-12
15:1
15:19
10.4230/LIPIcs.SWAT.2020.15
article
Low-Stretch Spanning Trees of Graphs with Bounded Width
Borradaile, Glencora
1
Chambers, Erin Wolf
2
Eppstein, David
3
Maxwell, William
1
Nayyeri, Amir
1
Oregon State University, Corvallis, OR, USA
Saint Louis University, MO, USA
University of California, Irvine, CA, USA
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol162-swat2020/LIPIcs.SWAT.2020.15/LIPIcs.SWAT.2020.15.pdf
Treewidth
low-stretch spanning tree
fundamental cycle basis