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A linear algorithm for the all-bidirectional-edges problem on planar graphs

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Abstract

The all-bidirectional-edges problem is to find an edge-labeling of an undirected networkG=(V, E), with a source and a sink, such that an edgee=uv inE is labeled 〈u, v〉 or 〈u, u〉 (or both) depending on the existence of a (simple) path from the source to the sink traversinge, that visits the verticesu andv in the orderu, v orv, u respectively. The best-known algorithm for this problem requiresO(¦V¦·¦E¦) time [5]. We show that the problem is solvable optimally on a planar graph.

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Authors and Affiliations

  1. Department of Computer Science and Engineering, Indian Institute of Technology, 600036, Madras, India

    P. B. Ramprasad & C. Pandu Rangan

Authors
  1. P. B. Ramprasad
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  2. C. Pandu Rangan
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Communicated by Christos H. Papadimitriou.

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Ramprasad, P.B., Pandu Rangan, C. A linear algorithm for the all-bidirectional-edges problem on planar graphs. Algorithmica 9, 199–216 (1993). https://doi.org/10.1007/BF01190896

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  • DOI: https://doi.org/10.1007/BF01190896

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