Reverse Shortest Path Problem in Weighted Unit-Disk Graphs

Wang, Haitao; Zhao, Yiming

doi:10.1007/978-3-030-96731-4_12

Cited by 3 publications

(1 citation statement)

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“…Note that reverse/inverse shortest path problems have been studied in the literature under various problem settings. Roughly speaking, the problems are to modify the graph (e.g., modify some edge weights) so that certain desired constraints related to shortest paths 1 Our algorithms for the L2 unweighted case were included in [34]; our results for the L2 weighted case have been presented in the 29th Fall Workshop on Computational Geometry (FWCG 2021) and has also been accepted in [36]. Note that the second algorithm for the L2 unweighted case runs in O(n 5/4 log 2 n) time in [34]; in this full version, we slightly improve the time to O(n 5/4 log 7/4 n) by changing the threshold for defining large cells from n 3/4 to (n/ log n) 3/4 in Section 4.…”

Section: Introductionmentioning

confidence: 99%

Reverse Shortest Path Problem for Unit-Disk Graphs

Wang

Zhao

2021

Lecture Notes in Computer Science

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Given a set P of n points in the plane, the unit-disk graph G r (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: computing the smallest r such that the shortest path length between s and t in G r (P ) is at most λ. In this paper, we present an algorithm of O( λ • n log n) time and another algorithm of O(n 5/4 log 7/4 n) time for the unweighted case, as well as an O(n 5/4 log 5/2 n) time algorithm for the weighted case.

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