An Ω(n) lower bound on the number of cell crossings for weighted shortest paths in d-dimensional polyhedral structures

Bauernöppel, Frank; Maheshwari, Anil; Sack, Jörg-Rüdiger

doi:10.1016/j.comgeo.2022.101897

Computational Geometry

2022

DOI: 10.1016/j.comgeo.2022.101897

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An Ω(n) lower bound on the number of cell crossings for weighted shortest paths in d-dimensional polyhedral structures

Frank Bauernöppel

Anil Maheshwari

Jörg-Rüdiger Sack

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2024

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Path Planning in a Weighted Planar Subdivision Under the Manhattan Metric

Davoodi,

Safari

2024

Graphs and Combinatorics

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In this paper, we consider the problem of path planning in a weighted polygonal planar subdivision. Each polygon has an associated positive weight which shows the cost of path per unit distance of movement in that polygon. The goal is to find a minimum cost path under the Manhattan metric for two given start and destination points. First, we propose an $$O(n^2)$$ O ( n 2 ) time and space algorithm to solve this problem, where n is the total number of vertices in the subdivision. Then, we improve the time and space complexity of the algorithm to $$O(n \log ^2 n)$$ O ( n log 2 n ) and $$O(n \log n)$$ O ( n log n ) , respectively, by applying a divide and conquer approach. We also study the case of rectilinear regions in three dimensions and show that the minimum cost path under the Manhattan metric is obtained in $$ O(n^2 \log ^3 n) $$ O ( n 2 log 3 n ) time and $$ O(n^2 \log ^2 n) $$ O ( n 2 log 2 n ) space.

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Path Planning in a Weighted Planar Subdivision Under the Manhattan Metric

Davoodi,

Safari

2024

Graphs and Combinatorics

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show abstract

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An Ω(n) lower bound on the number of cell crossings for weighted shortest paths in d-dimensional polyhedral structures

Cited by 1 publication

References 16 publications

Path Planning in a Weighted Planar Subdivision Under the Manhattan Metric

Path Planning in a Weighted Planar Subdivision Under the Manhattan Metric

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