Abstract
Proposed algorithms for calculating the shortest paths such as Dijikstra and Flowd-Warshall’s algorithms are limited to small networks due to computational complexity and cost. We propose an efficient and a more accurate approximation algorithm that is applicable to large scale networks. Our algorithm iteratively constructs levels of hierarchical networks by a node condensing procedure to construct hierarchical graphs until threshold. The shortest paths between nodes in the original network are approximated by considering their corresponding shortest paths in the highest hierarchy. Experiments on real life data show that our algorithm records high efficiency and accuracy compared with other algorithms.
Highlights
The internet and its associated technologies have changed the way society conducts businesses, and the way that families and friends relate with each other
Rattgan et al [7] designed a network structure index (NSI) algorithm to estimate the shortest path in networks by storing data in a structure
If there is path between central nodes of s and t, and shortest path between s and t is not recorded at the topmost hierarchy, the algorithm returns a path value of 0, which means there is no edge between s and t that is no path between s and t
Summary
The internet and its associated technologies have changed the way society conducts businesses, and the way that families and friends relate with each other. Computing the shortest path between any two nodes in a network is one of the most important concerns of researchers since it has a great potential for mobilizing people [5] Exact algorithms such as Dijkstra’s and Floyd-Warshall’s algorithms have not performed so well on large scale networks due to their high computational complexity. Saeed Maleki [10] proposed the Dijkstra strip mined relation (DSMR) algorithm for calculating the single source shortest path in networks With their approach, the entire network graph is passed to a distributor engine which slices the graph into subgraphs equal to the number of processors so that all subgraphs have approximately the same number of edges. Experimental results show that the runtime per query is only a few milliseconds on large networks, while accuracy is still maintained
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