Every Property Is Testable on a Natural Class of Scale-Free Multigraphs

Author Hiro Ito

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Hiro Ito

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Hiro Ito. Every Property Is Testable on a Natural Class of Scale-Free Multigraphs. In 24th Annual European Symposium on Algorithms (ESA 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 57, pp. 51:1-51:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)


In this paper, we introduce a natural class of multigraphs called hierarchical-scale-free (HSF) multigraphs, and consider constant-time testability on the class. We show that a very wide subclass of HSF is hyperfinite. Based on this result, an algorithm for a deterministic partitioning oracle can be constructed. We conclude by showing that every property is constant-time testable on the above subclass of HSF. This algorithm utilizes findings by Newman and Sohler of STOC'11. However, their algorithm is based on a bounded-degree model, while it is known that actual scale-free networks usually include hubs, which have a very large degree. HSF is based on scale-free properties and includes such hubs. This is the first universal result of constant-time testability on a class of graphs made by a model of scale-free networks, and it has the potential to be applicable on a very wide range of scale-free networks.
  • constant-time algorithms
  • scale-free networks
  • complex networks
  • isolated cliques
  • hyperfinite


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