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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
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.
References
Aref WG, Samet H (1990) Efficient processing of window queries in the pyramid data structure. In: Proceedings of the 9th ACM SIGACT-SIGMOD-SIGART symposium on principles of database systems (PODS), Nashville, pp 265–272
Chen Z, Shen H, Zhou X, Yu J (2009) Monitoring path nearest neighbor in road networks. In: Proceedings of the 35th SIGMOD international conference on management of data (SIGMOD’09), pp 591–602
Demiryurek U, Banaei-Kashani F, Shahabi C (2009) Efficient continuous nearest neighbor query in spatial networks using Euclidean restriction. In: Proceedings of the 11th international symposium on advances in spatial and temporal databases (SSTD’09), Lecture notes in computer science, vol 5644. Springer, pp 25–43
Dijkstra E (1959) A note on two problems in connection with graphs. Numer Math 1:269–271
Frederickson G (1987) Fast algorithms for shortest paths in planar graphs, with applications. SIAM J Comput 16(6):1004–1022
Goldberg A, Harrelson C (2005) Computing the shortest path: \(a^*\) search meets graph theory. In: Proceedings of the 16th annual ACM-SIAM symposium on discrete algorithms, pp 156–165
Goodrich M (1992) Planar separators and parallel polygon triangulation. In: Proceedings of the 24th ACM symposium on theory of computing, pp 507–516
Henzinger M, Klein P, Rao S, Subramanian S (1997) Faster shortest-path algorithms for planar graphs. J Comput Syst Sci 55(1):3–23
Jing N, Huang YW, Rundensteiner E (1998) Hierarchical encoded path views for path query processing: an optimal model and its performance evaluation. IEEE Trans Knowl Data Eng 10(3):409–432
Kolahdouzan, M, Shahabi C (2004) Voronoi-based \(k\) nearest neighbor search for spatial network databases. In: Proceedings of the 30th international conference on very large databases, Toronto, pp 840–851
Lipton R, Tarjan R (1979) A separator theorem for planar graphs. SIAM J Appl Math 36:177–189
Samet H, Alborzi H, Brabec F, Esperança C, Hjaltason GR, Morgan F, Tanin E (2003) Use of the SAND spatial browser for digital government applications. Commun ACM 46(1):63–66
Samet H, Sankaranarayanan J, Alborzi H (2011) Scalable network distance browsing in spatial databases. In: Proceedings of the 2008 ACM SIGMOD international conference on management of data (SIGMOD’08), pp 43–54
Sankaranarayanan J, Samet H (2009) Distance oracles for spatial networks. Shanghai, pp 652–663
Sankaranarayanan J, Samet H (2010) Query processing using distance oracles for spatial networks. 22(8):1158–1175, best Papers of ICDE 2009 Special Issue
Sankaranarayanan J, Samet H (2010) Roads belong in databases. 33(2):4–11, invited paper
Sankaranarayanan J, Alborzi H, Samet H (2005) Efficient query processing on spatial networks. In: Proceedings of the 13th ACM international symposium on advances in geographic information systems, Bremen, pp 200–209
Sankaranarayanan J, Alborzi H, Samet H (2006) Distance join queries on spatial networks. In: Proceedings of the 14th ACM international symposium on advances in geographic information systems, Arlington, pp 211–218
Sankaranarayanan J, Samet H, Alborzi H (2009) Path oracles for spatial networks. In: Proceedings of the VLDB endowment, Maynooth, pp 1210–1221
Shaffer CA, Samet H, Nelson RC (1990) QUILT: a geographic information system based on quadtrees 4(2), 103–131, also University of Maryland Computer Science Technical Report TR-1885
Shekhar S, Fetterer A, Goyal B (1997) Materialization trade-offs in hierarchical shortest path algorithms. In: Scholl M, Voisard A (eds) Proceedings of the 5th international symposium on advances in spatial databases (SSD’97), Lecture notes in computer science, vol 1262. Springer, pp 94–111
Sivan R, Samet H (1992) Algorithms for constructing quadtree surface maps. In: Proceedings of the 5th international symposium on spatial data handling. vol 1. Charleston, pp 361–370
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
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
Download citation
DOI: https://doi.org/10.1007/978-3-642-32316-4_4
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-32315-7
Online ISBN: 978-3-642-32316-4
eBook Packages: Earth and Environmental ScienceEarth and Environmental Science (R0)