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(nlog² n) and requires O(nlog n) 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(log n) time. The time complexity of our algorithm is a significant improvement over all previous results known for the shortest path problem