Relative interleavings and applications to sensor networks

Yasuaki Hiraoka, Genki Kusano

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

In this paper, we prove several results on interleavings for persistent relative homology of sub-level sets, (Formula presented.) complexes and Rips complexes. To prove the relative interleavings for (Formula presented.) complexes and Rips complexes, we define a relative correspondence which is related to the Gromov-Hausdorff distance. We also apply the relative Rips interleaving to a coverage problem in sensor networks, and show that the interleaving captures some features about the sensors after perturbation from the information of the unperturbed system.

Original languageEnglish
Pages (from-to)99-120
Number of pages22
JournalJapan Journal of Industrial and Applied Mathematics
Volume33
Issue number1
DOIs
Publication statusPublished - 2016 Feb 1

Keywords

  • Persistent homology
  • Sensor networks

ASJC Scopus subject areas

  • Engineering(all)
  • Applied Mathematics

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