Abstract
Finding the \(k\)-median in a network involves identifying a subset of k vertices that minimize the total distance to all other vertices in a graph. While known to be computationally challenging (NP-hard) several approximation algorithms have been proposed, most with high-order polynomial-time complexity. However, the graph topology of complex networks with heavy-tailed degree distributions present characteristics that can be exploited to yield custom-tailored algorithms. We compare eight algorithms specifically designed for complex networks and evaluate their performance based on accuracy and efficiency for problems of varying sizes and application areas. Rather than relying on a small number of problems, we conduct over 16,000 experiments covering a wide range of network sizes and \(k\)-median values. While individual results vary, a few methods provide consistently good results. We draw general conclusions about how algorithms perform in practice and provide general guidelines for solutions.
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Notes
- 1.
Certain commercial products or company names are identified here to describe our study adequately. Such identification does not imply recommendation or endorsement by the National Institute of Standards and Technology, nor does it imply that the products or names identified are necessarily the best available for the purpose.
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Pozo, R. (2024). Approximation Algorithms for k-Median Problems on Complex Networks: Theory and Practice. In: Cherifi, H., Rocha, L.M., Cherifi, C., Donduran, M. (eds) Complex Networks & Their Applications XII. COMPLEX NETWORKS 2023. Studies in Computational Intelligence, vol 1143. Springer, Cham. https://doi.org/10.1007/978-3-031-53472-0_8
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