Abstract
This chapter proposes the concept of critical time points, which are the time points at which the shortest path between a source-destination pair (in a spatio-temporal graph) changes. We formalize this concept through the problem of all-start-time Lagrangian shortest path (ALSP) problem. Using the idea of critical-time-points, we discuss an algorithm, called CTAS, for the ALSP problem. This chapter also establishes the correctness and completeness of CTAS.
This is a preview of subscription content, log in via an institution to check access.
Notes
- 1.
Note: an interval (a,b) does not include the end points a and b, [a,b] includes the endpoints a and b, and [a,b) includes a but not b.
- 2.
By stationarity, we mean that ranking of the alternate paths between a particular source-destination pair does not change within the interval i.e, there is a unique shortest path.
- 3.
In this chapter we would use the term shortest path and earliest arrival path interchangeably.
References
Ding, B., Yu, J., Qin, L.: Finding time-dependent shortest paths over large graphs. In: Proceedings of the 11th International Conference on Extending Database Technology: Advances in Database Technology, pp. 205–216. ACM, Nantes (2008)
George, B., Kim, S., Shekhar, S.: Spatio-temporal network databases and routing algorithms: a summary of results. In: Proceedings of the 10th International Conference on Advances in Spatial and Temporal Databases, SSTD’07, pp. 460–477. Springer, Berlin/Heidelberg (2007)
Gunturi, V.M.V., Shekhar, S., Bhattacharya, A.: Minimum spanning tree on spatio-temporal networks. In: Proceedings of the 21st International Conference on Database and Expert Systems Applications: Part II, DEXA’10, pp. 149–158 (2010)
Gunturi, V.M.V., Nunes, E., Yang, K., Shekhar, S.: A critical-time-point approach to all-start-time lagrangian shortest paths: a summary of results. In: Advances in Spatial and Temporal Databases. Lecture Notes in Computer Science, vol. 6849, pp. 74–91. Springer, Berlin/Heidelberg (2011)
Gunturi, V.M.V., Shekhar, S., Yang, K.: A critical-time-point approach to all-departure-time lagrangian shortest paths. IEEE Trans. Knowl. Data Eng. 27(10), 2591–2603 (2015)
Kanoulas, E., Du, Y., Xia, T., Zhang, D.: Finding fastest paths on a road network with speed patterns. In: Proceedings of the 22nd International Conference on Data Engineering (ICDE), p. 10. IEEE, Atlanta (2006)
Kaufman, D.E., Smith, R.L.: Fastest paths in time-dependent networks for intelligent vehicle-highway systems application. I V H S J. 1(1), 1–11 (1993)
Kleinberg, J., Tardos, E.: Algorithm Design. Pearson Education, London (2009)
Köhler, E., Langkau, K., Skutella, M.: Time-expanded graphs for flow-dependent transit times. In: Proceedings of the 10th Annual European Symposium on Algorithms, ESA ’02, pp. 599–611. Springer, London (2002)
NAVTEQ: Retrieved Oct 2017, https://www.here.com/en/navteq
Orda, A., Rom, R.: Shortest-path and minimum-delay algorithms in networks with time-dependent edge-length. J. ACM 37(3), 607–625 (1990)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this chapter
Cite this chapter
Gunturi, V.M.V., Shekhar, S. (2017). Advanced Concepts: Critical Time Point Based Approaches. In: Spatio-Temporal Graph Data Analytics. Springer, Cham. https://doi.org/10.1007/978-3-319-67771-2_5
Download citation
DOI: https://doi.org/10.1007/978-3-319-67771-2_5
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-67770-5
Online ISBN: 978-3-319-67771-2
eBook Packages: Computer ScienceComputer Science (R0)