An Hierarchical Terrain Representation for Approximately Shortest Paths

We propose a fast algorithm for on-line path search in grid-like undirected planar graphs with real edge costs (aka terrains). Our algorithm depends on an off-line analysis of the graph, requiring poly-logarithmic time and space. The off-line preprocessing constructs a hierarchical representation which allows detection of features specific to the terrain. While our algorithm is not guaranteed to find an optimal path, we demonstrate empirically that it is very fast, and that the difference from optimal is almost always small.