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On the hardness of approximating spanners

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Approximation Algorithms for Combinatiorial Optimization (APPROX 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1444))

Abstract

A k-spanner of a connected graph G = (V, E) is a subgraph G' consisting of all the vertices of V and a subset of the edges, with the additional property that the distance between any two vertices in G' is larger than that distance in G by no more than a factor of k. This paper concerns the hardness of finding spanners with the number of edges close to the optimum. It is proved that for every fixed k approximating the spanner problem is at least as hard as approximating the set cover problem

We also consider a weighted version of the spanner problem. We prove that in the case k=2 the problem admits an O(log n)-ratio approximation, and in the case k ≥ 5, there is no \(2^{log^{1 - \in } n}\)-ratio approximation, for any ε > 0, unless NP c DTIME(n polylog n).

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Authors and Affiliations

  1. Department of Computer Science, The Open university, Klauzner 16, Ramat Aviv, Israel

    Guy Kortsarz

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  1. Guy Kortsarz
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Klaus Jansen José Rolim

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© 1998 Springer-Verlag Berlin Heidelberg

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Kortsarz, G. (1998). On the hardness of approximating spanners. In: Jansen, K., Rolim, J. (eds) Approximation Algorithms for Combinatiorial Optimization. APPROX 1998. Lecture Notes in Computer Science, vol 1444. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0053970

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  • DOI: https://doi.org/10.1007/BFb0053970

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64736-2

  • Online ISBN: 978-3-540-69067-2

  • eBook Packages: Springer Book Archive

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