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Social Interactions and Networking in Cyber Society pp 199–207Cite as

Extended Algorithm for Travelling Salesman Problem with Conditions in Nodes

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Abstract

The paper describes a new algorithm for finding the shortest path in the graph among all nodes. The algorithm is based on the sequential removing of nodes from the graph. After removing a node, it is necessary to generate new edges that represent all paths through the node. This procedure maintains the configuration of the graph. The newly created edges are referred to as composed edges. The newly generated edges can be connected together only with simple (original) edges, because this could lead to overlaping the edges of the original graph and thus may occur incorrect paths in the graph. During the algorithm proceeds the continuous optimization of the edges so that it removes loops around the nodes. This leads to a significant reduction of the number of combinations of edges, and it simplifies the process. The algorithm was tested though procedure in Python and its complexity is polynomial time. The job is known as a problem of a Salesman or a Hamiltonian path or Hamiltonian circle in the graph. Results of proposed method can be used in logistics (distribution of goods among locations), in transport planning (selection of the optimal route between given points) in crisis management (optimal route for intervention in case of fire or accidents) in tourism and related services (planning the shortest route trip) or spatial analyses in geographic information systems (GIS).

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Acknowledgments

This paper was elaborated with the support of Brno University of Technology, Specific Research Projects FAST-S-15-2723 and FAST-S-16-3507.

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Authors and Affiliations

  1. Institute of Geodesy, Faculty of Civil Engineering, Brno University of Technology, Brno, Czech Republic

    Dalibor Bartoněk

  2. European Polytechnic Institute, Kunovice, Czech Republic

    Dalibor Bartoněk

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  1. Dalibor Bartoněk
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Correspondence to Dalibor Bartoněk .

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Editors and Affiliations

  1. Bina Nusantara University, Jakarta, Indonesia

    Ford Lumban Gaol

  2. University of Malaya, Kuala Lumpur, Malaysia

    Fonny Dameaty Hutagalung

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Bartoněk, D. (2017). Extended Algorithm for Travelling Salesman Problem with Conditions in Nodes. In: Gaol, F., Hutagalung, F. (eds) Social Interactions and Networking in Cyber Society. Springer, Singapore. https://doi.org/10.1007/978-981-10-4190-7_16

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  • DOI: https://doi.org/10.1007/978-981-10-4190-7_16

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-10-4189-1

  • Online ISBN: 978-981-10-4190-7

  • eBook Packages: Social SciencesSocial Sciences (R0)

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