NP-Completeness Results for Minimum Planar Spanners

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1996
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Handke, Dagmar
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Konstanzer Schriften in Mathematik und Informatik
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For any fixed parameter t>=1, a t-spanner of a graph G is a spanning subgraph in which the distance between every pair of vertices is at most t times their distance in G. A minimum t-spanner is a t-spanner with minimum total edge weight or, in unweighted graphs, minimum number of edges. In this paper, we prove the NP-hardness of finding minimum t-spanners for planar weighted graphs and digraphs if t>=3, and for planar unweighted graphs and digraphs if t>=5. We thus extend results on that problem to the interesting case where the instances are known to be planar. We also introduce the related problem of finding minimum planar t-spanners and establish its NP-hardness for similar fixed values of t.

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004 Informatik
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ISO 690BRANDES, Ulrik, Dagmar HANDKE, 1996. NP-Completeness Results for Minimum Planar Spanners
BibTex
@techreport{Brandes1996NPCom-6371,
  year={1996},
  series={Konstanzer Schriften in Mathematik und Informatik},
  title={NP-Completeness Results for Minimum Planar Spanners},
  number={16},
  author={Brandes, Ulrik and Handke, Dagmar}
}
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