TY - JOUR

T1 - On the hardness of approximating spanners

AU - Kortsarz, Guy

N1 - Copyright:
Copyright 2017 Elsevier B.V., All rights reserved.

PY - 2001/7

Y1 - 2001/7

N2 - 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 the distance in G by no more than a factor of k. This paper concerns the hardness of finding spanners with a 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, and prove an essential difference between the approximability of the case k = 2 and the case k ≥ 5.

AB - 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 the distance in G by no more than a factor of k. This paper concerns the hardness of finding spanners with a 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, and prove an essential difference between the approximability of the case k = 2 and the case k ≥ 5.

KW - Graph spanners

KW - Hardness of approximation

UR - http://www.scopus.com/inward/record.url?scp=0242269933&partnerID=8YFLogxK

U2 - 10.1007/s00453-001-0021-y

DO - 10.1007/s00453-001-0021-y

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AN - SCOPUS:0242269933

SN - 0178-4617

VL - 30

SP - 432

EP - 450

JO - Algorithmica

JF - Algorithmica

IS - 3

ER -