Computing the Point-to-Point Shortest Path: Quotient Space Theory’s Application in Complex Network

Abstract

The quotient space theory can represent the world at different granularity sizes and deal with complicated problems hierarchically. We present significant improvement to point-to-point shortest path based on quotient space theory in complex large-scale network. We propose the shortest path algorithm that is a heuristic method, in which evaluation function is based on community and hierarchical granularity decomposition of quotient space theory. In preprocessing, we decompose large-scale network into some communities using hierarchical granularity decomposition of quotient space theory, compute and store the minimum spanning trees in the communities and the shortest distance among communities. The implementation works on the large-scale road network. From experimental results, we know the proposed algorithm is effective and efficient in the road network of US.