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We present an algorithm to find an {\it Euclidean Shortest Path} from asource vertex $s$ to a sink vertex $t$ in the presence of obstacles in $\Re^2$.Our algorithm takes $O(T+m(\lg{m})(\lg{n}))$ time and $O(n)$ space. Here,$O(T)$ is the time to triangulate the polygonal region, $m$ is the number ofobstacles, and $n$ is the number of vertices. This bound is close to the knownlower bound of $O(n+m\lg{m})$ time and $O(n)$ space. Our approach involveprogressing shortest path wavefront as in continuous Dijkstra-type method, andconfining its expansion to regions of interest.

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