Simplicial homology and wireless networks

Speaker : Anais Vergne
Telecom ParisTech
Date: 22/10/2014
Time: 2:00 pm - 2:30 pm
Location: LINCS Meeting Room 40


Simplicial complex representation gives a mathematical description ofthe topology of a wireless sensor network, i.e., its connectivity andcoverage. In these networks, sensors are randomly deployed in bulk inorder to ensure perfect connectivity and coverage. We propose analgorithm to discover which sensors are to be switched off, withoutmodification of the topology, in order to reduce energy consumption.Our reduction algorithm can be applied to any type of simplicialcomplex and reaches an optimal solution.In a second part, we consider a damaged wireless network, presentingcoverage holes or disconnected components, wepropose a disaster recovery algorithm repairing the network. Itprovides the list of locations where to put new nodes topatch the coverage holes and mend the disconnected components. Inorder to do this we first consider the simplicial complexrepresentation of the network, then the algorithm adds supplementarynodes in excessive number, and afterwards runs the reduction algorithmin order to reach a unimprovable result. We use a determinantal pointprocess for the addition of nodes: the Ginibre point process which hasinherent repulsion between vertices.