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Arc Routing Based on the Zero-Suppressed Binary Decision Diagram

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Abstract

A wide range of problems in operations research falls under arc routing problems, a domain which focuses on arc or edge features rather than node or vertex attributes. The undirected rural postman problem is a well-known problem in arc routing that seeks to determine a minimum cost walk that traverses a certain set of required edges on a given graph. The problem, arising in numerous real-world applications, is nondeterministic polynomial-time hard. The chapter presents a solution to the undirected rural postman problem based on the zero-suppressed binary decision diagram, a compact data structure that represents a family of sets. Through an extension to the frontier-based search method of diagram construction, the approach solves the problem by efficient enumeration, producing all feasible routes in addition to the optimal route. Instances of the problem put forward in literature are then solved as benchmark for the decision-diagram-based solution. As reasonable time is consumed, the method proves to be a practicable candidate in solving the undirected rural postman problem.

Keywords

  • Arc routing
  • Enumeration algorithm
  • Frontier-based search
  • Graph optimization
  • Rural postman problem
  • Zero-suppressed binary decision diagram

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Notes

  1. 1.

    https://csacademy.com/app/graph_editor/.

  2. 2.

    https://github.com/kunisura/TdZdd.

  3. 3.

    https://github.com/renzopereztan/ZDDLines.

  4. 4.

    https://github.com/renzopereztan/URPDD.

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Acknowledgements

The research is supported by the Japan Society for the Promotion of Science through the Grants-in-Aid for Scientific Research Program (KAKENHI 18K19821). Valuable advice was received from Jun Kawahara. J. Kawahara is with the Kyoto University, Japan and the Nara Institute of Science and Technology, Japan. Further, Miguel Zenon Nicanor L. Saavedra has provided assistance in implementation. M. Z. N. L. Saavedra is with the Trainocate Group, Philippines and the Ateneo de Manila University, Philippines.

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Correspondence to Renzo Roel P. Tan .

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Tan, R.R.P., Sikora, F., Ikeda, K., See, K.S.S. (2021). Arc Routing Based on the Zero-Suppressed Binary Decision Diagram. In: Ao, SI., Gelman, L., Kim, H.K. (eds) Transactions on Engineering Technologies. Springer, Singapore. https://doi.org/10.1007/978-981-15-8273-8_9

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  • DOI: https://doi.org/10.1007/978-981-15-8273-8_9

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