Coresets of obstacles in approximating Euclidean shortest path amid convex obstacles

Given a set P of non-intersecting polygonal obstacles in R defined with n vertices, we compute a sketch Ω of P whose size is independent of n. We utilize Ω to devise an algorithm to compute a (1 + )-approximate Euclidean shortest path between two points given with the description of P. When P comprises of convex polygonal obstacles, we devise a (2 + )approximation algorithm to efficiently answer two-point Euclidean distance queries.