A New Algorithm for Euclidean Shortest Paths in the Plane

Given a set of pairwise disjoint polygonal obstacles in the plane, finding an obstacle-avoiding Euclidean shortest path between two points is classical problem computational geometry and has been studied extensively. Previously, Hershberger Suri (in SIAM Journal on Computing , 1999) gave algorithm O(n log n ) time space, where total number vertices all obstacles. Recently, by modifying Suri’s algorithm, Wang SODA’21) reduced space to O(n) while runtime still ). In this article, we present new O(n+h h provided that triangulation free given, The better than previous work when relatively small. Our builds map for source point s so given any query t length from can be computed O (log - produced additional linear edges path.