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
(
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.
Publisher
Springer Science and Business Media LLC
Subject
Discrete Mathematics and Combinatorics,Theoretical Computer Science
Reference34 articles.
1. Davoodi, M., Enamzadeh, H., Safari, A.: Path planning in a weighted planar subdivision under the Manhattan metric. In: CCCG, pp. 80–86 (2020)
2. Olcay, E., Schuhmann, F., Lohmann, B.: Collective navigation of a multi-robot system in an unknown environment. Robot. Auton. Syst. 132, 103604 (2020)
3. Davoodi, M., Abedin, M., Banyassady, B., Khanteimouri, P., Mohades, A.: An optimal algorithm for two robots path planning problem on the grid. Robot. Auton. Syst. 61(12), 1406–1414 (2013)
4. Davoodi, M.: Bi-objective path planning using deterministic algorithms. Robot. Auton. Syst. 93, 105–115 (2017)
5. Davoodi, M., Rouhani, A., Sanisales, M.: Path planning with objectives minimum length and maximum clearance. In: International Conference on Topics in Theoretical Computer Science, pp. 101–115. Springer (2020)