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On the second point-to-point undirected shortest simple path problem

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Abstract

We address the determination of the second point-to-point shortest simple path in undirected networks. The effective reduced cost concept is introduced to compute the second best solution. This concept is used to prove that a path tree containing the second point-to-point shortest simple path is adjacent to any shortest path tree. Therefore, this result immediately implies a method requiring O(m) time once that the shortest path tree is obtained on an undirected network with n nodes and m edges.

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Authors and Affiliations

  1. Departamento de Estadística, Investigación Operativa y Computación Universidad de La Laguna, 38271, La Laguna, Tenerife, Spain

    Antonio Sedeño-Noda & Carlos González-Martín

Authors
  1. Antonio Sedeño-Noda
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  2. Carlos González-Martín
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Correspondence to Antonio Sedeño-Noda.

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Sedeño-Noda, A., González-Martín, C. On the second point-to-point undirected shortest simple path problem. Optim Lett 7, 1875–1881 (2013). https://doi.org/10.1007/s11590-012-0528-y

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  • DOI: https://doi.org/10.1007/s11590-012-0528-y

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