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Distributed protocols for ensuring both coverage and connectivity of a wireless sensor network

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Fig. 1. Determining the perimeter coverage of a sensor s i .
Fig. 2. Proof of Lemma 1: (a) the path construction, and (b) possible cases of s x .
Fig. 3. Observations of Theorem 2 and Theorem 3: (a) the network is 2-covered and 1-connected
Fig. 5. An example that k-LDPC is looser than k-DPC.
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