An optimal algorithm for L1 shortest paths in unit-disk graphs

Wang, Haitao; Zhao, Yiming

doi:10.1016/j.comgeo.2022.101960

Cited by 1 publication

(2 citation statements)

References 16 publications

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“…The SSSP algorithms of [7,8] for the L 2 unweighted version can be easily adapted to the L 1 unweighted version. Wang and Zhao [33] recently solved the L 1 weighted case in O(n log n) time. It is known that Ω(n log n) is a lower bound for the SSSP problem in both L 1 and L 2 versions [7,33].…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Introductionmentioning

confidence: 99%

“…Wang and Zhao [33] recently solved the L 1 weighted case in O(n log n) time. It is known that Ω(n log n) is a lower bound for the SSSP problem in both L 1 and L 2 versions [7,33]. Hence, the SSSP problem in the L 1 weighted/unweighted case as well as in the L 2 unweighted case has been solved optimally.…”

Section: Introductionmentioning

confidence: 99%

Reverse Shortest Path Problem for Unit-Disk Graphs

Wang

Zhao

2021

Lecture Notes in Computer Science

View full text Add to dashboard Cite

show abstract

An optimal algorithm for L1 shortest paths in unit-disk graphs

Cited by 1 publication

References 16 publications

Reverse Shortest Path Problem for Unit-Disk Graphs

Reverse Shortest Path Problem for Unit-Disk Graphs

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