Random Abstract Simplicial Complexes Reduction

Anaïs Vergne; Laurent Decreusefond; Philippe Martins

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arXiv · 1312.1658

Random Abstract Simplicial Complexes Reduction

Anaïs Vergne·Laurent Decreusefond·Philippe Martins

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Abstract

Random abstract simplicial complex representation provides a mathematical description of wireless networks and their topology. In order to reduce the energy consumption in this type of network, we intend to reduce the number of network nodes without modifying neither the connectivity nor the coverage of the network. In this paper, we present a reduction algorithm that lower the number of points of an abstract simplicial complex in an optimal order while maintaining its topology. Then, we study the complexity of such an algorithm for a network simulated by a binomial point process and represented by a Vietoris-Rips complex.

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Anaïs Vergne, Laurent Decreusefond, Philippe Martins. 2013-12-05. Random Abstract Simplicial Complexes Reduction. https://arxiv.org/abs/1312.1658

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