Parametric Shortest Paths in a Linearly Interpolated Graph

Jacob Sriraman; Eli Barton; Brittany Terese Fasy; David L. Millman; Brendan Mumey; Nate Rengo; Braeden Sopp; Vasishta Tumuluri; Binhai Zhu

arXiv · 2604.08892

Parametric Shortest Paths in a Linearly Interpolated Graph

Jacob Sriraman·Eli Barton·Brittany Terese Fasy·David L. Millman·Brendan Mumey·Nate Rengo·Braeden Sopp·Vasishta Tumuluri·Binhai Zhu

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Abstract

We consider the parametric shortest paths problem in a linearly interpolated graph. Given two positively-weighted directed graphs $G_0=(V,E,\omega_0)$ and $G_1=(V,E,\omega_1),$ the linearly interpolated graph is the family of graphs $(1-\lambda)G_0+\lambda G_1$, parameterized by $\lambda\in [0,1]$. The problem is to compute all distinct parametric shortest paths. We compute a data structure in $\Theta(k|E|\log |V|)$ time, where~$k$ is the number of distinct parametric shortest paths over all~$\lambda\in [0,1]$ that exist for a nontrivial interval of parameters, each corresponding to a linear function in a maximal sub-interval of $[0,1]$. Using this data structure, a shortest path query takes~$\Theta(\log k)$ time.

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BibTeX RIS

Jacob Sriraman, Eli Barton, Brittany Terese Fasy, David L. Millman, Brendan Mumey, Nate Rengo, Braeden Sopp, Vasishta Tumuluri, Binhai Zhu. 2026-04-10. Parametric Shortest Paths in a Linearly Interpolated Graph. https://arxiv.org/abs/2604.08892

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