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Approximating Metric Spaces by Tree Metrics

1996; Bartal, Fakcharoenphol, Rao, Talwar 2004; Bartal, Fakcharoenphol, Rao, Talwar

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Encyclopedia of Algorithms

Keywords and Synonyms

Embedding general metrics into tree metrics          

Problem Definition

This problem is to construct a random tree metric that probabilistically approximates a given arbitrary metric well. A solution to this problem is useful as the first step for numerous approximation algorithms because usually solving problems on trees is easier than on general graphs. It also finds applications in on-line and distributed computation.

It is known that tree metrics approximate general metrics badly, e. g., given a cycle C n with n nodes, any tree metric approximating this graph metric has distortion \( { \Omega(n) } \) [17]. However, Karp [15] noticed that a random spanning tree of C n approximates the distances between any two nodes in C n well in expectation. Alon, Karp, Peleg, and West [1] then proved a bound of \( { \exp(O(\sqrt{\log n\log\log n})) } \) on an average distortion for approximating any graph metric with its spanning tree.

Bartal [2] formally defined the notion of...

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Recommended Reading

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Author information

Authors and Affiliations

  1. Department of Computer Engineering, Kasetsart University, Bangkok, Thailand

    Jittat Fakcharoenphol

  2. Computer Science Division, University of California at Berkeley, Berkeley, CA, USA

    Satish Rao

  3. Microsoft Research, Silicon Valley Campus, Mountain View, CA, USA

    Kunal Talwar

Authors
  1. Jittat Fakcharoenphol
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  2. Satish Rao
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  3. Kunal Talwar
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Editor information

Editors and Affiliations

  1. Department of Electrical Engineering and Computer ScienceMcCormick School of Engineering and Applied Science, Northwestern University, Evanston, IL, 60208, USA

    Ming-Yang Kao Professor of Computer Science

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© 2008 Springer-Verlag

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Fakcharoenphol, J., Rao, S., Talwar, K. (2008). Approximating Metric Spaces by Tree Metrics. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-30162-4_25

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