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Abstract

Network scaling algorithms such as the Pathfinder algorithm are used to prune many different kinds of networks, including citation networks, random networks, and social networks. However, this algorithm suffers from run time problems for large networks and online processing due to its O(n**4) time complexity. In this article, we introduce a new alternative, the MST-Pathfinder algorithm, which will allow us to prune the original network to get its PFNET(oo, n - 1) in just O(n**2 · log n) time. The underlying idea comes from the fact that the union (superposition) of all the Minimum Spanning Trees extracted from a given network is equivalent to the PFNET resulting from the Pathfinder algorithm parameterized by a specific set of values (r = oo and q = n - 1), those usually considered in many different applications. Although this property is well-known in the literature, it seems that no algorithm based on it has been proposed, up to now, to decrease the high computational cost of the original Pathfinder algorithm. We also present a mathematical proof of the correctness of this new alternative and test its good efficiency in two different case studies: one dedicated to the post-processing of large random graphs, and the other one to a real world case in which medium networks obtained by a cocitation analysis of the scientific domains in different countries are pruned.

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Abstract

In the last few years, there is an increasing interest to generate visual representations of very large scientific domains. A methodology based on the combined use of ISI-JCR category cocitation and social networks analysis through the use of the Pathfinder algorithm has demonstrated its ability to achieve high quality, schematic visualizations for these kinds of domains. Now, the next step would be to generate these scientograms in an on-line fashion. To do so, there is a need to significantly decrease the run time of the latter pruning technique when working with category cocitation matrices of a large dimension like the ones handled in these large domains (Pathfinder has a time complexity order of O(n4), with n being the number of categories in the cocitation matrix, i.e., the number of nodes in the network). Although a previous improvement called Binary Pathfinder has already been proposed to speed up the original algorithm, its significant time complexity reduction is not enough for that aim. In this paper, we make use of a different shortest path computation from classical approaches in computer science graph theory to propose a new variant of the Pathfinder algorithm which allows us to reduce its time complexity in one order of magnitude, O(n3), and thus to significantly decrease the run time of the implementation when applied to large scientific domains considering the parameter q = n - 1. Besides, the new algorithm has a much simpler structure than the Binary Pathfinder as well as it saves a significant amount of memory with respect to the original Pathfinder by reducing the space complexity to the need of just storing two matrices. An experimental comparison will be developed using large networks from real-world domains to show the good performance of the new proposal.

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