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The MinSum-MinHop and the MaxMin-MinHop Bicriteria Path Problems

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Shortest Path Solvers. From Software to Wetware

Part of the book series: Emergence, Complexity and Computation ((ECC,volume 32))

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Abstract

The number of hops (or arcs) of a path is a frequent objective function with applications to problems where network resources utilization is to be minimized. In this chapter we solve bicriteria path problems involving this objective function and two other common metrics, the path cost and the path capacity. Labeling algorithms are introduced, which use a breadth-first search tree in order to compute the maximal and the minimal sets of non-dominated paths. Dominance rules are derived for the two bicriteria problems and the properties of this data structure are explored to better suit the number of hops objective function and thus simplify the labeling process. Computational experiments comparing the new methods with standard approaches on randomly generated test instances and on instances that simulate video traffic are presented and discussed. Results show a significant speed-up over generic standard methods.

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Acknowledgements

This work was partially supported by the Institute for Systems Engineering and Computers at Coimbra – UID/MULTI/00308/2013, the Centre for Mathematics of the University of Coimbra – UID/MAT/00324/2013, and the grant SFRH/BSAB/113683/2015, funded by the Portuguese Government through FCT/MEC and co-funded by the European Regional Development Fund through the Partnership Agreement PT2020.

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Authors and Affiliations

  1. CMUC, Department of Mathematics, University of Coimbra, 3001-501, Coimbra, Portugal

    Marta Pascoal

  2. Institute for Systems and Computers Engineering, Coimbra, Portugal

    Marta Pascoal

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  1. Marta Pascoal
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Correspondence to Marta Pascoal .

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Editors and Affiliations

  1. Unconventional Computing Centre, University of the West of England, Bristol, United Kingdom

    Andrew Adamatzky

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Pascoal, M. (2018). The MinSum-MinHop and the MaxMin-MinHop Bicriteria Path Problems. In: Adamatzky, A. (eds) Shortest Path Solvers. From Software to Wetware. Emergence, Complexity and Computation, vol 32. Springer, Cham. https://doi.org/10.1007/978-3-319-77510-4_3

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  • DOI: https://doi.org/10.1007/978-3-319-77510-4_3

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-77509-8

  • Online ISBN: 978-3-319-77510-4

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