Low-stretch spanning trees of graphs with bounded width
arXiv preprint arXiv:2004.08375, 2020•arxiv.org
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 $\mathcal T $ of
spanning trees such that the expected stretch of each edge of $ G $ is $ O (b^ 2) $. Our proof
implies a linear time algorithm for sampling from $\mathcal T $. Therefore, we have a linear
time algorithm that finds a spanning tree of $ G $ with average stretch $ O (b^ 2) $ with high …
cutwidth, and treewidth. We show that any simple connected graph $ G $ with a linear
arrangement of bandwidth $ b $ can be embedded into a distribution $\mathcal T $ of
spanning trees such that the expected stretch of each edge of $ G $ is $ O (b^ 2) $. Our proof
implies a linear time algorithm for sampling from $\mathcal T $. Therefore, we have a linear
time algorithm that finds a spanning tree of $ G $ with average stretch $ O (b^ 2) $ with high …
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 with a linear arrangement of bandwidth can be embedded into a distribution of spanning trees such that the expected stretch of each edge of is . Our proof implies a linear time algorithm for sampling from . Therefore, we have a linear time algorithm that finds a spanning tree of with average stretch with high probability. We also describe a deterministic linear-time algorithm for computing a spanning tree of with average stretch . For graphs of cutwidth , we construct a spanning tree with stretch in linear time. Finally, when has treewidth we provide a dynamic programming algorithm computing a minimum stretch spanning tree of that runs in polynomial time with respect to the number of vertices of .
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