A NEAR-OPTIMAL ALGORITHM FOR SHORTEST PATHS AMONG CURVED OBSTACLES IN THE PLANE

Date

2022-01-01

Author

Hershberger, John
Suri, Subhash
Yıldız, Hakan

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© 2022 Society for Industrial and Applied Mathematics.We propose an algorithm for the problem of computing shortest paths among curved obstacles in the plane. If the obstacles have O(n) description complexity, then the algorithm runs in O(n log n) time plus a term dependent on the properties of the boundary arcs. Specifically, if the arcs allow a certain kind of bisector intersection to be computed in constant time, or even in O(log n) time, then the running time of the overall algorithm is O(n log n). If the arcs support only constant-time tangent, intersection, and length queries, as is customarily assumed, then the algorithm computes an approximate shortest path, with relative error ε, in time O(n log n + n log 1\e ). In fact, the algorithm computes an approximate shortest path map, a data structure with O(n log n) size, that allows it to report the (approximate) length of a shortest path from a fixed source point to any query point in the plane in O(log n) time. By applying an idea due to Wang [Proceedings of the 32nd Annual ACM-SIAM Symposium on Discrete Algorithms, 2021, pp. 810-821], the algorithm's working storage and the size of the approximate shortest path map can be reduced to O(n).

Subject Keywords

geometric obstacles, obstacle avoidance, planar subdivision, shortest path map, shortest paths

URI

https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85137634523&origin=inward
https://hdl.handle.net/11511/100846

Journal

SIAM Journal on Computing

DOI

https://doi.org/10.1137/21m1428248

Collections

Department of Computer Engineering, Article

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Citation Formats

J. Hershberger, S. Suri, and H. Yıldız, “A NEAR-OPTIMAL ALGORITHM FOR SHORTEST PATHS AMONG CURVED OBSTACLES IN THE PLANE,” SIAM Journal on Computing, vol. 51, no. 4, pp. 1296–1340, 2022, Accessed: 00, 2022. [Online]. Available: https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85137634523&origin=inward.