Original Paper

Applicable Algebra in Engineering, Communication and Computing

, Volume 23, Issue 1, pp 29-58

First online:

Open Access This content is freely available online to anyone, anywhere at any time.

Distributed computation of coverage in sensor networks by homological methods

  • P. DłotkoAffiliated withInstitute of Computer Science, Jagiellonian University
  • , R. GhristAffiliated withDepartments of Mathematics and Electrical & Systems Engineering, University of Pennsylvania
  • , M. JudaAffiliated withInstitute of Computer Science, Jagiellonian University
  • , M. MrozekAffiliated withInstitute of Computer Science, Jagiellonian UniversityDivision of Computational Mathematics, WSB-NLU Email author 


Recent work on algebraic-topological methods for verifying coverage in planar sensor networks relied exclusively on centralized computation: a limiting constraint for large networks. This paper presents a distributed algorithm for homology computation over a sensor network, for purposes of verifying coverage. The techniques involve reduction and coreduction of simplicial complexes, and are of independent interest. Verification of the ensuing algorithms is proved, and simulations detail the improved network efficiency and performance.


Homology Sensor network Coverage Distributed computation

Mathematics Subject Classification

55-04 55N99 52B99