Videos

Homological Methods for Quantifying Coverage in Dynamic Sensor Networks

Presenter
March 6, 2014
Keywords:
  • Homological Methods, sequence
MSC:
  • 46M18
Abstract
A dynamic sensor network may be represented as a sequence of simplicial complexes, and analyzed using zigzag persistent homology, with the resulting barcode containing birth-death intervals for homological features of the sequence. In this talk I will first describe the relationship between these intervals and the time-varying coverage holes in the network, as well as the scenarios in which the zigzag persistence barcode works well as a coverage descriptor. Further, I will propose a method for making a geometrically-relevant choice of representative cycle for each feature at its birth and/or death time, and propagating that information over the entire interval. This can allow “tracking” of the coverage holes in the network. Additionally, these representative cycles are used in conjunction with a hop-distance filtration to determine size estimates for the holes over time. This estimated size information is then used to enhance the regular barcode, giving a visual and quantitative descriptor of the time-varying network coverage.