Abstract
A hierarchical approach to the single-pair shortest path problem subdivides a network with \(n\) vertices into \(r\) regions with the same number \(m\) of vertices (\(n = r m\)) and iteratively creates higher levels of a hierarchical network by merging a constant number \(c\) of adjacent regions. In a hierarchical approach, shortest paths are computed at higher levels and expanded towards lower levels through intra-regional queries. We introduce a hybrid shortest path algorithm to perform intra-regional queries. This strategy uses a subsequence of pre-processed vertices that belong to the shortest path while actually computing the whole shortest path. At the lowest level, the hybrid algorithm requires \(O(m)\) time and space assuming a uniform distribution of vertices. For higher levels, the path view approach takes \(O(1)\) time and requires \(O(c^k m)\) space.
This work was supported in part by the National Science Foundation under Grants IIS-10-18475, IIS-09-48548, IIS-08-12377, and CCF-08-30618.
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Notes
- 1.
We assume without loss of generality that \(r\) is a power of \(c\), i.e., \(r = c^h\), where \(h\) is the highest level in the hierarchy of networks.
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Guerra-Filho, G., Samet, H. (2013). A Hybrid Shortest Path Algorithm for Intra-Regional Queries on Hierarchical Networks. In: Timpf, S., Laube, P. (eds) Advances in Spatial Data Handling. Advances in Geographic Information Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32316-4_4
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