TY - GEN

T1 - On the hardness of approximating spanners

AU - Kortsarz, Guy

N1 - Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 1998.

PY - 1998

Y1 - 1998

N2 - A k-spanner of a connected graph G = (V, E) is a subgraph Gʹ 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 Gʹ 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 2log1-ϵ n-ratio approximation, for any ϵ > 0, unless NP ⊆ DTIME(npolylog n).

AB - A k-spanner of a connected graph G = (V, E) is a subgraph Gʹ 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 Gʹ 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 2log1-ϵ n-ratio approximation, for any ϵ > 0, unless NP ⊆ DTIME(npolylog n).

UR - http://www.scopus.com/inward/record.url?scp=84958968556&partnerID=8YFLogxK

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U2 - 10.1007/BFb0053970

DO - 10.1007/BFb0053970

M3 - Conference contribution

AN - SCOPUS:84958968556

SN - 3540647368

SN - 9783540647362

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 135

EP - 146

BT - Approximation Algorithms for Combinatorial Optimization - International Workshop, APPROX 1998, Proceedings

A2 - Rolim, José

A2 - Jansen, Klaus

PB - Springer Verlag

T2 - International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 1998

Y2 - 18 July 1998 through 19 July 1998

ER -