A New Algorithm for Euclidean Shortest Paths in the Plane

Document Type

Conference Paper

Author ORCID Identifier

Haitao Wang https://orcid.org/0000-0001-8134-7409

Journal/Book Title/Conference

ACM SIGACT Symposium on Theory of Computing 2021


Association for Computing Machinery

Publication Date


Award Number

NSF, Division of Computing and Communication Foundations (CCF) 2005323


NSF, Division of Computing and Communication Foundations (CCF)

First Page


Last Page



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. Previously, Hershberger and Suri [SIAM J. Comput. 1999] gave an algorithm of O(nlogn) time and O(nlogn) space, where n is the total number of vertices of all obstacles. Recently, by modifying Hershberger and Suri’s algorithm, Wang [SODA 2021] reduced the space to O(n) while the runtime of the algorithm is still O(nlogn). In this paper, we present a new algorithm of O(n+hlogh) time and O(n) space, provided that a triangulation of the free space is given, where h is the number of obstacles. Our algorithm 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.