Computing the Dynamic Diameter of Non-Deterministic Dynamic Networks is Hard
نویسندگان
چکیده
A dynamic network is a communication network whose communication structure can evolve over time. The dynamic diameter is the counterpart of the classical static diameter, it is the maximum time needed for a node to causally influence any other node in the network. We consider the problem of computing the dynamic diameter of a given dynamic network. If the evolution is known a priori, that is if the network is deterministic, it is known it is quite easy to compute this dynamic diameter. If the evolution is not known a priori, that is if the network is non-deterministic, we show that the problem is hard to solve or approximate. In some cases, this hardness holds also when there is a static connected subgraph for the dynamic network. In this note, we consider an important subfamily of non-deterministic dynamic networks: the time-homogeneous dynamic networks. We prove that it is hard to compute and approximate the value of the dynamic diameter for time-homogeneous dynamic networks.
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