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DIMACS Theory of Computing Seminar

Planar Distance Oracles

Seth Pettie (U Mich)

Date & time: Wednesday, 28 October 2020 at 11:00AM - 12:00PM

Abstract: We consider the problem of preprocessing a weighted planar graph in order to answer exact distance and shortest path queries. As in the recent algorithms of Cohen-Addad et al. (2017), Gawrychowski et al. (2018), and Charalampopoulos et al. (2019), our algorithm is based on solving the point-location problem in weighted planar Voronoi diagrams.

We give a new, efficient method to solve point location using persistent data structures, which leads to a new time-space tradeoff for the problem. At the extremes of this tradeoff, the data structure: * occupies \(n^{1+o(1)}\) space and answers distance queries in \(log^{2+o(1)} n\) time, or

* occupies \(nlog^{2+o(1)} n\) space and answers distance queries in \(n^{o(1)}\) time.

Joint work with Yaowei Long, to appear in SODA 2021. arXiv:2007.08585.

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