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Near-optimal Steiner tree computation powered by node embeddings

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Abstract

Steiner minimum tree problem on a graph, i.e., finding a tree with the minimum weight that covers the set of terminal nodes, is a classical NP-hard problem. Thus, we develop a method based on supervised learning to produce a near-optimal Steiner tree in this paper. It contains three main phases, namely node embedding, candidate set generation, and tree construction. Leveraged on compressed sensing, we devise a novel node embedding that exhibits a good nature of reversibility for sparse linear aggregations, which powers learning a mapping function from the terminal set to the optimal Steiner tree. Finally, we propose efficient pruning techniques to improve the solution quality. The experimental results show that our approach delivers high-quality solutions and runs faster than the competitors by one or two orders of magnitude on graphs with more than 200 nodes.

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The datasets used in the paper can be found at the following link: http://steinlib.zib.de/steinlib.php.

Notes

  1. http://steinlib.zib.de/steinlib.php.

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Funding

This work was substantially supported by the National Natural Science Foundation of China (Grant No. 61902074). The authors have no relevant financial or non-financial interests to disclose.

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  1. School of Data Science, Fudan University, Shanghai, China

    Boyu Yang & Weiguo Zheng

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  1. Boyu Yang
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All authors contributed to the study conception and design. BY was involved in methodology, writing, and evaluation. WZ was involved in conceptualization of this study, methodology, writing, and editing.

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Correspondence to Weiguo Zheng.

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Yang, B., Zheng, W. Near-optimal Steiner tree computation powered by node embeddings. Knowl Inf Syst 65, 4563–4583 (2023). https://doi.org/10.1007/s10115-023-01893-8

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