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Ranking One Million Simple Paths in Road Networks

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  • Antonio Sedeño-Noda

    (Departamento de Matemáticas, Estadística e Investigación Operativa, Universidad de La Laguna, C. P. 38271, San Cristóbal de La Laguna, Santa cruz de Tenerife, España)

Abstract

In this paper, we address the problem of finding the K best paths connecting a given pair of nodes in a directed graph with arbitrary lengths. We introduce an algorithm to determine the K best paths in order of length when repeat nodes in the paths are allowed. We obtain an O(m + nlog n + K(n +log K)) time and O(K + m) space algorithm to implicitly determine the K shortest paths in a directed graph with n nodes and m arcs. Empirical results where the algorithm was used to compute one hundred million paths in USA road networks are reported. A non-trivial modification of the previous algorithm is performed obtaining an O(k1(nm +log k1)) time method to compute paths without repeat nodes and to answer the next question: how many paths k1 in practice are needed to identify K simple paths using the previous algorithm? We find that the response is usually O(K) based on an experiment computing one million paths in USA road networks. The determination of a theoretical tight bound on k1 remains as an open problem.

Suggested Citation

  • Antonio Sedeño-Noda, 2016. "Ranking One Million Simple Paths in Road Networks," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 33(05), pages 1-20, October.
    • Handle: RePEc:wsi:apjorx:v:33:y:2016:i:05:n:s0217595916500421
    DOI: 10.1142/S0217595916500421
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    References listed on IDEAS

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    1. Jin Y. Yen, 1971. "Finding the K Shortest Loopless Paths in a Network," Management Science, INFORMS, vol. 17(11), pages 712-716, July.
    2. Eugene L. Lawler, 1972. "A Procedure for Computing the K Best Solutions to Discrete Optimization Problems and Its Application to the Shortest Path Problem," Management Science, INFORMS, vol. 18(7), pages 401-405, March.
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