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Range Query on Planar Graphs and Applications on Spatial Sensing with Privacy
Jie Gao, Rutgers
Date & time: Wednesday, 16 September 2020 at 11:00AM - 12:00PM
Abstract: We consider the problem of performing counting range queries on a planar graph G. Suppose each edge e in G has a value v(e) and a length w(e). We would like to ask the following queries: what is the sum of the values from the edges on the shortest path from u to v? The goal is to perform preprocessing into a data structure with subquadratic storage such that each query can be answered in sublinear time. We show that one could use a data structure of size O(n\log n^2) such that each query can be answered in time O(log n). This data structure also has application in enabling differentially privacy queries on spatial sensing data. It could also be extended to support 2D queries, where the range is a collection of faces in G whose boundary is enclosed by k shortest paths.
The work is joint with Abhirup Ghosh, Jiaxin Ding, and Rik Sarkar.