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On the Shortest Route Through a Network

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  • George B. Dantzig

    (The RAND Corporation)

Abstract

The chief feature of the method is that it fans out from the origin working out the shortest path to one new node from the origin and never having to backtrack. No more than n(n-1)/2 comparisons are needed to find the shortest route from a given origin to all other nodes and possibly less between two fixed nodes. Except for details and bias of various authors towards a particular brand of proof, this problem has been solved the same way by many authors. This paper refines these proposals to give what is believed to be the shortest procedure for finding the shortest route when it is little effort to arrange distances in increasing order by nodes or to skip consideration of arcs into nodes whose shortest route to the origin has been determined earlier in the computation. In practice the number of comparisons is much less than indicated bounds because all arcs leading to nodes previously evaluated are deleted from further consideration. A further efficiency can be achieved in the event of ties by including least distances from origin to many nodes simultaneously during the fanning out process. However, these are shown as separate steps to illustrate the underlying principle.

Suggested Citation

  • George B. Dantzig, 1960. "On the Shortest Route Through a Network," Management Science, INFORMS, vol. 6(2), pages 187-190, January.
    • Handle: RePEc:inm:ormnsc:v:6:y:1960:i:2:p:187-190
    DOI: 10.1287/mnsc.6.2.187
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    Cited by:

    1. Lee, Jisun & Joung, Seulgi & Lee, Kyungsik, 2022. "A fully polynomial time approximation scheme for the probability maximizing shortest path problem," European Journal of Operational Research, Elsevier, vol. 300(1), pages 35-45.
    2. Huang, He & Gao, Song, 2012. "Optimal paths in dynamic networks with dependent random link travel times," Transportation Research Part B: Methodological, Elsevier, vol. 46(5), pages 579-598.
    3. Tadao Takaoka, 2013. "A simplified algorithm for the all pairs shortest path problem with O(n 2logn) expected time," Journal of Combinatorial Optimization, Springer, vol. 25(2), pages 326-337, February.
    4. Anirudh Kishore Bhoopalam & Niels Agatz & Rob Zuidwijk, 2023. "Platoon Optimization Based on Truck Pairs," INFORMS Journal on Computing, INFORMS, vol. 35(6), pages 1242-1260, November.
    5. Elías Escobar-Gómez & J.L. Camas-Anzueto & Sabino Velázquez-Trujillo & Héctor Hernández-de-León & Rubén Grajales-Coutiño & Eduardo Chandomí-Castellanos & Héctor Guerra-Crespo, 2019. "A Linear Programming Model with Fuzzy Arc for Route Optimization in the Urban Road Network," Sustainability, MDPI, vol. 11(23), pages 1-18, November.
    6. Santos, Luis & Coutinho-Rodrigues, João & Current, John R., 2007. "An improved solution algorithm for the constrained shortest path problem," Transportation Research Part B: Methodological, Elsevier, vol. 41(7), pages 756-771, August.
    7. Su, Jason G. & Winters, Meghan & Nunes, Melissa & Brauer, Michael, 2010. "Designing a route planner to facilitate and promote cycling in Metro Vancouver, Canada," Transportation Research Part A: Policy and Practice, Elsevier, vol. 44(7), pages 495-505, August.
    8. Linzhong Liu & Haibo Mu & Juhua Yang, 2017. "Toward algorithms for multi-modal shortest path problem and their extension in urban transit network," Journal of Intelligent Manufacturing, Springer, vol. 28(3), pages 767-781, March.
    9. Hughes, Michael S. & Lunday, Brian J. & Weir, Jeffrey D. & Hopkinson, Kenneth M., 2021. "The multiple shortest path problem with path deconfliction," European Journal of Operational Research, Elsevier, vol. 292(3), pages 818-829.
    10. I-Lin Wang & Ellis L. Johnson & Joel S. Sokol, 2005. "A Multiple Pairs Shortest Path Algorithm," Transportation Science, INFORMS, vol. 39(4), pages 465-476, November.
    11. Zionts, Stanley, 1962. "Methods for Selection of an Optimum Route," Transportation Research Forum Conference Archive 316265, Transportation Research Forum.
    12. Wang, Li & Yang, Lixing & Gao, Ziyou, 2016. "The constrained shortest path problem with stochastic correlated link travel times," European Journal of Operational Research, Elsevier, vol. 255(1), pages 43-57.
    13. Luigi Di Puglia Pugliese & Francesca Guerriero, 2016. "On the shortest path problem with negative cost cycles," Computational Optimization and Applications, Springer, vol. 63(2), pages 559-583, March.
    14. Richard W. Cottle, 2005. "George B. Dantzig: Operations Research Icon," Operations Research, INFORMS, vol. 53(6), pages 892-898, December.
    15. Kishore Bhoopalam, A. & Agatz, N.A.H. & Zuidwijk, R.A., 2020. "Spatial and Temporal Synchronization of Truck Platoons," ERIM Report Series Research in Management ERS-2020-014-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.

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