Maximum number of independent paths and radio connectivity

Methods for determining the network reliability of a multihop packet radio network in the presence of hostile jammers are discussed. A new connectivity parameter called radio connectivity is defined as the maximum number of disjoint communication paths that are still usable between given nodes s and d after the jammer is on or, more generally, the minimum number of jammers needed to disconnect s and d. A lower bound on the radio connectivity is computed by studying the number of jamming independent paths. The time complexity of obtaining the radio connectivity is analyzed and shown to be NP-hard except for some special cases. Greedy heuristics for developing approximate answers for general networks are described. Euclidean networks, in which the nodes and links correspond to points and line segments in the Euclidean geometry and satisfy Euclid's four fundamental axioms, are also discussed. It is found that the maximum number of independent paths between a pair of source and destination nodes that can possibly exist is five. An extension in which there is a protected zone of known size around the sender and receiver is studied.<
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