Abstract
AbstractIn 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
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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 $$O(n \log ^2 n)$$
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and $$O(n \log n)$$
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, 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
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n
2
log
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time and $$ O(n^2 \log ^2 n) $$
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space.
Publisher
Springer Science and Business Media LLC
Reference34 articles.
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