Identifying Hierarchies for Fast Optimal Search

For some search problems, the graph is known beforehand and there is time to preprocess the graph to make the search faster. One such example is video games, where one can often preprocess maps before a game is released or while a map is loaded into memory. The data produced by preprocessing should use only a small amount of memory, and, in case they are generated during runtime, preprocessing should be fast. Search with Subgoal Graphs (Uras, Koenig, and Hernández 2013) was a non-dominated optimal path-planning algorithm in the Grid-Based Path Planning Competitions 2012 and 2013. During a preprocessing phase, it computes a Simple Subgoal Graph from a given grid, which is analogous to a visibility graph for continuous terrain, and then partitions the vertices into global and local subgoals to obtain a Two-Level Subgoal Graph. During the path-planning phase, it performs an A* search over the subgoal graph that ignores local subgoals that are not relevant to the search, which significantly reduces the size of the graph being searched. This paper is an abstract of (Uras and Koenig 2014), which generalizes this partitioning process to any undirected graph and shows that it can be recursively applied to generate more than two levels, which reduces the size of the graph being searched even further. We call these graphs N-Level Graphs.