# Shortest Paths Among Obstacles in the Plane Revisited

@article{Wang2020ShortestPA, title={Shortest Paths Among Obstacles in the Plane Revisited}, author={Haitao Wang}, journal={ArXiv}, year={2020}, volume={abs/2010.09115} }

Given a set of pairwise disjoint polygonal obstacles in the plane, finding an obstacle-avoiding Euclidean shortest path between two points is a classical problem in computational geometry and has been studied extensively. The previous best algorithm was given by Hershberger and Suri [FOCS 1993, SIAM J. Comput. 1999] and the algorithm runs in $O(n\log n)$ time and $O(n\log n)$ space, where $n$ is the total number of vertices of all obstacles. The algorithm is time-optimal because $\Omega(n\log n…

## 2 Citations

### A new algorithm for Euclidean shortest paths in the plane

- Computer Science, MathematicsSTOC
- 2021

This paper builds a shortest path map for a source point s, so that given any query point t, the shortest path length from s to t can be computed in O(logn) time and a shortest s-t path can be produced in additional time linear in the number of edges of the path.

### Coverage Path Planning and Precise Localization for Autonomous Lawn Mowers

- Computer Science2022 Sixth IEEE International Conference on Robotic Computing (IRC)
- 2022

Two objectives contribute to the increased efficiency of the presented approach compared to classical automatic lawn mowing techniques.

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