A low-stretch spanning tree T in a graph G is a spanning tree for G with the additional constraint that the distance between any two vertices in T is at most a small constant factor times the distance between the two same vertices in G. In other words, the tree does not “stretch” distances too much.
Feb 3, 2017
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E.g., they can be used to more efficiently solve “Laplacian” linear systems of the form A⃗x = ⃗b, where A is the Laplacian matrix of some graph G.
The Star De- composition algorithm takes a graph and recursively divides it into smaller parts until we create a low-stretch spanning tree. Most of the ...
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Nov 17, 2004 · Abstract: We prove that every weighted graph contains a spanning tree subgraph of average stretch O((log n log log n)^2).
Apr 22, 2016 · A basic tool that is often used in constructing tree metrics and spanning trees with low stretch is sparse graph decomposition. The idea is to ...
In this lecture, we show how to construct low-stretch trees. This is a bit out of order because we have not yet said why having low-stretch trees is useful ...
Abstract. We study the problem of low-stretch spanning trees in graphs of bounded width: bandwidth, cutwidth, and treewidth.
Apr 13, 2018 · Spanning trees of low average stretch on the non-tree edges, as introduced by Alon et al. [SICOMP 1995], are a natural graph-theoretic object.
Dec 6, 2006 · In this lecture we study the topic of approximating arbitrary graph metrics by (efficiently sample- able) distributions over spanning subtrees.
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We have implemented a variant of the algorithm of Alon, Karp, Peleg and West for computing low stretch spanning trees. It is called akpw.