Organizer(s):

Sepehr Assadi, Rutgers University

Swastik Kopparty, Rutgers University

Jie Gao, Rutgers University

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(nlog 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.

The Theory of Computing Seminar is being held online. Contact the organizers for the link to the seminar.