### 摘要

Wireless sensor network (WSN) has been an active research topic because its application encompasses various domains. In particular, a lot of attention have been paid to the common feature of WSN to show that every node in a large enough network contains certain properties. Real-world applications of random key pre-distribution naturally involve geometric and combinatorial techniques and are even more challenging technically. This paper presents an efficient scheme, which can approximate a complex network by a much simpler object such that the approximation is "regular" between most pairs of partition of this network. Once a more traceable network is obtained, bounds for the probability of the property that a random key pre-distribution subgraph satisfies that each node has a path of length ℓ to its ℓth-hop neighbors are established. Then, by using the sparse version of Szemerédi's regularity lemma and letting C be a constant, n the number of vertices, p the probability of any two nodes sharing at least one common key, a sharp threshold p≥Cn^{-(ℓ-1)/ℓ} that satisfies this property is shown. Moreover, computer simulations are also given to show the performance of the proposed scheme.

原文 | English |
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頁（從 - 到） | 2776-2787 |

頁數 | 12 |

期刊 | Mathematical and Computer Modelling |

卷 | 57 |

發行號 | 11-12 |

DOIs | |

出版狀態 | Published - 2013 六月 1 |

### 指紋

### All Science Journal Classification (ASJC) codes

- Modelling and Simulation
- Computer Science Applications

### 引用此

*Mathematical and Computer Modelling*,

*57*(11-12), 2776-2787. https://doi.org/10.1016/j.mcm.2012.03.001