Reverse Shortest Path Problem for Unit-Disk Graphs
Algorithms and Data Structures
NSF, Division of Computing and Communication Foundations (CCF) 2005323
NSF, Division of Computing and Communication Foundations (CCF)
Given a set P of n points in the plane, a unit-disk graph Gr(P) with respect to a radius r is an undirected graph whose vertex set is P such that an edge connects two points p, q ∈ P is the number of edges of the path. Given a value λ > 0 and two points s and t of P, we consider the following reverse shortest path problem: finding the smallest r such that the shortest path length between s and t in Gr(P) is at most λ. It was known previously that the problem can be solved in O(n5/4log2n) time.
Wang, Haitao and Zhao, Yiming, "Reverse Shortest Path Problem for Unit-Disk Graphs" (2021). Computer Science Faculty and Staff Publications. Paper 36.