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Time-dependent shortest paths in bounded treewidth graphs.

arXiv: Data Structures and Algorithms(2017)

Cited 23|Views9
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Abstract
We present a proof that the number of breakpoints in the arrival function between two terminals in graphs of treewidth $w$ is $n^{O(log^2 w)}$ when the edge arrival functions are piecewise linear. This is an improvement on the bound of $n^{Theta(log n)}$ by Foschini, Hershberger, and Suri for graphs without any bound on treewidth. We provide an algorithm for calculating this arrival function using star-mesh transformations, a generalization of the wye-delta-wye transformations.
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