# Encyclopedia of Algorithms

2016 Edition
| Editors: Ming-Yang Kao

# Low Stretch Spanning Trees

Reference work entry
DOI: https://doi.org/10.1007/978-1-4939-2864-4_215

## Years and Authors of Summarized Original Work

• 2005; Elkin, Emek, Spielman, Teng

## Problem Definition

Consider a weighted connected multigraph G = ( V,  E,  ω), where ω is a function from the edge set E of G into the set of positive reals. For a path P in G, the weight of P is the sum of weights of edges that belong to the path P. For a pair of vertices u,  v ∈  V,the distance between them in G is the minimum weight of a path connecting u and v in G. For a spanning tree T of G, the stretch of an edge ( u, v) ∈  E is defined by
$$\displaystyle{ \mathrm{stretch}_{T}(u,v) = \frac{\mathrm{dist}_{T}(u,v)} {\mathrm{dist}_{G}(u,v)}, }$$

## Keywords

Spanning trees with low average stretch
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## Recommended Reading

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## Copyright information

© Springer Science+Business Media New York 2016

## Authors and Affiliations

1. 1.Department of Computer ScienceBen-Gurion UniversityBeer-ShevaIsrael