A Hybrid Shortest Path Algorithm for Intra-Regional Queries on Hierarchical Networks

A hierarchical approach to the single-pair shortest path problem subdivides a network with n vertices into r regions with the same number m of vertices (n = rm) and iteratively creates higher levels of a hierarchical network by merging a constant number c of adjacent regions. In a hierarchical approach, shortest paths are computed at higher levels and expanded towards lower levels through intra-regional queries. We introduce a hybrid shortest path algorithm to perform intra-regional queries. This strategy uses a subsequence of pre-processed vertices that belong to the shortest path while actually computing the whole shortest path. At the lowest level, the hybrid algorithm requires O(m) time and space assuming a uniform distribution of vertices. For higher levels, the path view approach takes O(1) time and requires O(cm) space.