A near optimal algorithm for finding Euclidean shortest path in polygonal domain

We present an algorithm to find an Euclidean Shortest Path from a source vertex s to a sink vertex t in the presence of obstacles in R. Our algorithm takes O(T +m(lgm)(lg n)) time and O(n) space. Here, O(T ) is the time to triangulate the polygonal region, m is the number of obstacles, and n is the number of vertices. This bound is close to the known lower bound of O(n+m lgm) time and O(n) space. Our approach involve progressing shortest path wavefront as in continuous Dijkstra-type method, and confining its expansion to regions of interest.