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.
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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.
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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
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DOI: https://doi.org/10.1007/978-3-319-67771-2_5
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