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Finding the Kth shortest path in a time‐schedule network

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  • Yen‐Liang Chen
  • Kwei Tang

Abstract

We consider the problem of finding the Kth shortest path for a time‐schedule network, where each node in the network has a list of prespecified departure times, and departure from the node can take place only at one of these departure times. We develop a polynomial time algorithm independent of K for finding the Kth shortest path. The proposed algorithm constructs a map structure at each node in the network, using which we can directly find the Kth shortest path without having to enumerate the first K − 1 paths. Since the same map structure is used for different K values, it is not necessary to reconstruct the table for additional paths. Consequently, the algorithm is suitable for directly finding multiple shortest paths in the same network. Furthermore, the algorithm is modified slightly for enumerating the first K shortest paths and is shown to have the lowest possible time complexity under a condition that holds for most practical networks. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2005.

Suggested Citation

  • Yen‐Liang Chen & Kwei Tang, 2005. "Finding the Kth shortest path in a time‐schedule network," Naval Research Logistics (NRL), John Wiley & Sons, vol. 52(1), pages 93-102, February.
    • Handle: RePEc:wly:navres:v:52:y:2005:i:1:p:93-102
    DOI: 10.1002/nav.20061
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    References listed on IDEAS

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    1. Martin Desrochers & Jacques Desrosiers & Marius Solomon, 1992. "A New Optimization Algorithm for the Vehicle Routing Problem with Time Windows," Operations Research, INFORMS, vol. 40(2), pages 342-354, April.
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    1. Jia, Jianlin & Chen, Yanyan & Wang, Yang & Li, Tongfei & Li, Yongxing, 2021. "A new global method for identifying urban rail transit key station during COVID-19: A case study of Beijing, China," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 565(C).

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