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A note on the 2-connectivity in one-dimensional ad hoc networks. (English) Zbl 1214.68050

Summary: 2-connectivity is the basic graph theoretical metric for fault tolerance to node failures, and it is an extremely desirable property in network design. For a one-dimensional finite ad hoc network formed by \(n\) nodes uniformly and independently distributed in a closed interval \([0,z]\) \((z \in \mathbb R^{+})\), we give a closed form expression for the probability that a connected one-dimensional finite ad hoc network becomes disconnected after removing a node. We also sketch a procedure of finding the exact formula for 2-connectivity in a one-dimensional ad hoc network.

MSC:

68M10 Network design and communication in computer systems
05C40 Connectivity
68R10 Graph theory (including graph drawing) in computer science
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References:

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