# Reverse Shortest Path Problem in Weighted Unit-Disk Graphs

## 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 ^{5/4}log^{5/2}n)* time algorithm. We also consider the

*L*version of the problem where the distance of two points is measured by the

_{1}*L*metric; we solve the problem in

_{1}*O(nlog*time for both the unweighted and weighted cases.

^{3}n)## 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