A New Algorithm for Optimal Path Finding in Complex Networks Based on the Quotient Space

The optimal path finding problem in weighted edge networks is an old and interesting one in many fields. There were many well-known algorithms to deal with that issue. But they were confronted with the high computational complexity while the network becoming larger. We present a hierarchical quotient space model based algorithm that reduces the computational complexity. The basic idea is the following. The nodes of a given network are partitioned with respect to the weights of their adjacent edges. We construct a variety of coarser versions of the given network with new nodes corresponding to the blocks of partitions at various levels of granularity. They are called the quotient spaces (networks) of the original network. The construction of the (sub) optimal path is then done incrementally, throughout the hierarchy of quotient networks. Since each version of the network is much simpler than the original one, especially of the coarsest spaces, the computational complexity is reduced. In this paper, we present the basic principles of the algorithm and its experimental comparison to other well-known algorithms.