New distributed shortest path algorithm for hierarchically clustered data networks
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This paper presents new efficient shortest path algorithms to solve single origin shortest path problems (SOSP problems) and multiple origins shortest path problems (MOSP problems) for a class of hierarchically clustered data networks with n nodes. The distributed version of our SOSP algorithm has the time complexity of O(log(n)), which is less than the time complexity of O(log2(n)) achieved by the best existing algorithm, for SOSP problems. Our MOSP algorithm minimizes the needed computation resources, which include computation processors and communication links, for each shortest path computation so that we can achieve massive parallelization. The parallel time complexity of our MOSP algorithm is O(mlog(n)), which is much less than the time complexity of (Mlog2(n)) of the best existing algorithm. Here, M is the number of the shortest paths to be computed and m is a positive number related to the network situations and is usually much smaller than M. We observe that m is almost a constant when the network size increases.