A Heuristic Approach for Shortest Path Problem With Rectilinear Obstacles.
Lim, Joon Shik · 1994
This dissertation presents new heuristic search algorithms, the Guided Minimum Detour (GMD) algorithm and the Line-by-Line Guided Minimum Detour (LGMD) algorithm for searching rectilinear ($L\sb1$) shortest paths in the presence of rectilinear obstacles. The GMD algorithm combines the best features of maze-running algorithms and line-search algorithms. The LGMD algorithm is a modification of the GMD algorithm that improves on efficiency using line-by-line extensions. Our GMD and LGMD algorithms always find a rectilinear shortest path using the guided $A\sp*$ search method without constructing a connection graph that contains a shortest path. The GMD algorithm and the LGMD algorithm can be implemented in $O(m + (e + N$)loge) and $O((e + N$)loge) time, respectively, and $O(e + N$) space, where m is the total number of searched nodes, e is the number of boundary sides of obstacles, and N is the total number of searched line segments. We consider the problem of finding a shortest path in terms of the number of bends and the combined length and bends.