Finding obstacle-avoiding shortest paths using implicit connection graphs

We introduce a framework for a class of algorithms solving shortest path related problems, such as the one-to-one shortest path problem, the one-to-many shortest paths problem and the minimum spanning tree problem, in the presence of obstacles. For these algorithms, the search space is restricted to a sparse strong connection graph that is implicitly represented and its searched portion is constructed incrementally on-the-fly during search. The time and space requirements of these algorithms essentially depend on actual search behavior. Therefore, additional techniques or heuristics can be incorporated into search procedure to further improve the performance of the algorithms. These algorithms are suitable for large VLSI design applications with many obstacles.