Efficient Computation of Euclidean Shortest Paths in the Plane

We propose a new algorithm for a classical problem in plane computational geometry: computing a shortest path between two points in the presence of polygonal obstacles. Our algorithm runs in worst-case time O(nlog2n) and requires O(n1ogn) space, where n is the total number of vertices in the obstacle polygons. Our algorithm actually computes a planar map that encodes shortest paths from a fixed source point to all other points of the plane; the map can be used to answer single-source shortest path queries in O(1og n) time. The time complexity of our algorithm is a significant improvement over all previous results known for the shortest path problem.