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

Z. Lipiński

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arXiv · 1402.2327

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

Z. Lipiński

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Abstract

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.

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Z. Lipiński. 2014-02-10. On the role of symmetry in solving maximum lifetime problem in two-dimensional sensor networks. https://arxiv.org/abs/1402.2327

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