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Algorithms for Spanners in Weighted Graphs

2003; Baswana, Sen

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Encyclopedia of Algorithms

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Keywords and Synonyms

Graph algorithms; Randomized algorithms; Shortest path; Spanner        

Problem Definition

A spanner is a sparse subgraph of a given undirected graph that preserves approximate distance between each pair of vertices. More precisely, a t-spanner of a graph \( { G=(V,E) } \) is a subgraph \( { (V,E_S), E_S\subseteq E } \) such that, for any pair of vertices, their distance in the subgraph is at most t times their distance in the original graph, where t is called the stretch factor. The spanners were defined formally by Peleg and Schäffer [14], though the associated notion was used implicitly by Awerbuch [3] in the context of network synchronizers.

Computing a t-spanner of smallest size for a given graph is a well motivated combinatorial problem with many applications. However, computing t-spanner of smallest size for a graph is NP-hard. In fact, for \( { t > 2 } \), it is NP-hard [10] even to approximate the smallest size of a t-spanner of a graph with ratio \( {...

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Notes

  1. 1.

    Ties can be broken arbitrarily. However, it helps conceptually to assume that all weights are distinct.

Recommended Reading

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Author information

Authors and Affiliations

  1. Department of Computer Science and Engineering, IIT Kanpur, Kanpur, India

    Surender Baswana

  2. Department of Computer Science and Engineering, IIT Delhi, New Delhi, India

    Sandeep Sen

Authors
  1. Surender Baswana
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  2. Sandeep Sen
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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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Baswana, S., Sen, S. (2008). Algorithms for Spanners in Weighted Graphs. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-30162-4_10

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