Sample Compression Schemes for Balls in Graphs

Authors Jérémie Chalopin, Victor Chepoi, Fionn Mc Inerney, Sébastien Ratel, Yann Vaxès

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Jérémie Chalopin
  • Aix-Marseille Université, Université de Toulon, CNRS, LIS, Marseille, France
Victor Chepoi
  • Aix-Marseille Université, Université de Toulon, CNRS, LIS, Marseille, France
Fionn Mc Inerney
  • CISPA Helmholtz Center for Information Security, Saarbrücken, Germany
Sébastien Ratel
  • Aix-Marseille Université, Université de Toulon, CNRS, LIS, Marseille, France
Yann Vaxès
  • Aix-Marseille Université, Université de Toulon, CNRS, LIS, Marseille, France

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Jérémie Chalopin, Victor Chepoi, Fionn Mc Inerney, Sébastien Ratel, and Yann Vaxès. Sample Compression Schemes for Balls in Graphs. In 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 241, pp. 31:1-31:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


One of the open problems in machine learning is whether any set-family of VC-dimension d admits a sample compression scheme of size O(d). In this paper, we study this problem for balls in graphs. For balls of arbitrary radius r, we design proper sample compression schemes of size 4 for interval graphs, of size 6 for trees of cycles, and of size 22 for cube-free median graphs. We also design approximate sample compression schemes of size 2 for balls of δ-hyperbolic graphs.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Graph algorithms
  • Theory of computation → Machine learning theory
  • Proper Sample Compression Schemes
  • Balls
  • Graphs
  • VC-dimension


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