A method for finding shortest paths is disclosed which uses a piecewise linear cost model to guide the search of through a compact tile graph and to ensure that a shortest path may always be found in a computationally effective manner. Cost function propagation from tile segment to tile segment is used to search for a target location from a source location through a region, and the shortest path is found through tracing backwards using the cost functions calculated during the searching. Linear minimal convolution is used to facilitate the cost function propagation.