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Learning a hidden graph

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Abstract

We study the problem of learning a hidden graph by edge-detecting queries, each of which tells whether a set of vertices induces an edge of the hidden graph or not. We provide a new information-theoretic lower bound and give a more efficient adaptive algorithm to learn a general graph with \(n\) vertices and \(m\) edges in \(m\log n+10m+3n\) edge-detecting queries.

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Acknowledgments

The authors would like to express their gratitude to the referees for their valuable comments and suggestions in improving the presentation of this paper. Partially supported by National Science Council, Taiwan under Grant NSC 99-2811-M-009-056 (H.-L. Fu and C.-H. Shih) and 100-2115-M-390-004-MY2 (H. Chang).

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Authors and Affiliations

  1. Department of Applied Mathematics, National University of Kaohsiung, Kaohsiung , 811, Taiwan, ROC

    Huilan Chang

  2. Department of Applied Mathematics, National Chiao Tung University, Hsinchu , 30010, Taiwan, ROC

    Hung-Lin Fu & Chih-Huai Shih

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  1. Huilan Chang
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  2. Hung-Lin Fu
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  3. Chih-Huai Shih
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Correspondence to Chih-Huai Shih.

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Chang, H., Fu, HL. & Shih, CH. Learning a hidden graph. Optim Lett 8, 2341–2348 (2014). https://doi.org/10.1007/s11590-014-0751-9

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  • DOI: https://doi.org/10.1007/s11590-014-0751-9

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