Reverse Shortest Path Problem in Weighted Unit-Disk Graphs

Authors

Haitao Wang, Utah State UniversityFollow
Yiming Zhao, Utah State University

Document Type

Article

Journal/Book Title/Conference

WALCOM: Algorithms and Computation

Volume

13174

Publisher

Springer

Publication Date

3-16-2022

Award Number

NSF, Division of Computing and Communication Foundations (CCF) 2005323

Funder

NSF, Division of Computing and Communication Foundations (CCF)

First Page

135

Last Page

146

Abstract

Given a set P of n points in the plane, a unit-disk graph Gr(P) with respect to a parameter r is an undirected graph whose vertex set is P such that an edge connects two points p,q∈P if the (Euclidean) distance between p and q is at most r (the weight of the edge is 1 in the unweighted case and is the distance between p and q in the weighted case). Given a value λ>0 and two points s and t of P, we consider the following reverse shortest path problem: Compute the smallest r such that the shortest path length between s and t in Gr(P) is at most λ. In this paper, we study the weighted case and present an O(n^5/4log^5/2n) time algorithm. We also consider the L₁ version of the problem where the distance of two points is measured by the L₁ metric; we solve the problem in O(nlog³n) time for both the unweighted and weighted cases.

Recommended Citation

Wang, Haitao and Zhao, Yiming, "Reverse Shortest Path Problem in Weighted Unit-Disk Graphs" (2022). Computer Science Faculty and Staff Publications. Paper 38.
https://digitalcommons.usu.edu/computer_science_facpubs/38