Mayer-Vietoris sequences and coverage problems in sensor networks

Zin Arai, Kazunori Hayashi, Yasuaki Hiraoka

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)

Abstract

Acoverage problem of sensor networks is studied. Following recentworks by Ghrist et al., in which computational topological methods are applied for the coverage problem, We present an algorithm for the distributed computation of the first homology group of planar Rips complexes. The key idea is to decompose a Rips complex into smaller pieces of subcomplexes, and to make use of Mayer-Vietoris sequences in order to sum up the homology groups of subcomplexes. Combined with a sufficient condition for the coverage which is given in terms of the first homology group, the proposed algorithm enables us to verify the coverage in a distributed manner.

Original languageEnglish
Pages (from-to)237-250
Number of pages14
JournalJapan Journal of Industrial and Applied Mathematics
Volume28
Issue number2
DOIs
Publication statusPublished - 2011 Aug

Keywords

  • Coverage problems
  • Mayer-Vietoris sequences
  • Sensor networks

ASJC Scopus subject areas

  • Engineering(all)
  • Applied Mathematics

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