6533b824fe1ef96bd1280cae

RESEARCH PRODUCT

On the role of symmetry in solving maximum lifetime problem in two-dimensional sensor networks

Zbigniew Lipinski

subject

Networking and Internet Architecture (cs.NI)FOS: Computer and information sciencesMathematical optimizationComputer scienceGroup (mathematics)Computer Networks and CommunicationsSymmetry groupInvariant (physics)TopologySymmetry (physics)Computer Science - Networking and Internet Architecturesymmetry groupEuclidean geometryHomogeneous spaceIsometryInvariant (mathematics)Electrical and Electronic Engineeringwireless sensor networksWireless sensor networkenergy efficiencyInformation Systems

description

We analyze a continuous and discrete symmetries of the maximum lifetime problem in two dimensional sensor networks. We show, how a symmetry of the network and invariance of the problem under a given transformation group $G$ can be utilized to simplify its solution. We prove, that for a $G$-invariant maximum lifetime problem there exists a $G$-invariant solution. Constrains which follow from the $G$-invariance allow to reduce the problem and its solution to a subset, an optimal fundamental region of the sensor network. We analyze in detail solutions of the maximum lifetime problem invariant under a group of isometry transformations of a two dimensional Euclidean plane.

10.1007/s11276-016-1354-4http://dx.doi.org/10.1007/s11276-016-1354-4