An extension of labeling techniques for finding shortest path trees |
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Authors: | Athanasios K Ziliaskopoulos Fotios D Mandanas Hani S Mahmassani |
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Institution: | 1. Systems Optimization Laboratory, Department of Mechanical and Industrial Engineering, University of Thessaly, Leoforos Athinon, Pedion Areos, 38334 Volos, Greece;2. Department of Civil and Environmental Engineering, University of Maryland, College Park, MD 20742-3021, USA |
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Abstract: | Label setting techniques are all based on Dijkstra’s condition of always scanning the node with the minimum label, which guarantees that each node will be scanned exactly once; while this condition is sufficient it is not necessary. In this paper, we discuss less restrictive conditions that allow the scanning of a node that does not have the minimum label, yet still maintaining sufficiency in scanning each node exactly once; various potential shortest path schemes are discussed, based on these conditions. Two approaches, a label setting and a flexible hybrid one are designed and implemented. The performance of the algorithms is assessed both theoretically and computationally. For comparative analysis purposes, three additional shortest path algorithms – the commonly cited in the literature – are coded and tested. The results indicate that the approaches that rely on the less restrictive optimality conditions perform substantially better for a wide range of network topologies. |
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Keywords: | Routing Transportation Shortest path |
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