  How to observe the state of a network from a limited number of measurements
has become an important issue in complex networks, engineering, communication,
epidemiology, etc. Under some scenarios, it is neither unfeasible nor
unnecessary to observe the entire network. Therefore, we investigate the target
observation of a network in this paper. We propose a target minimal dominating
set problem corresponding to target observation, which is a natural
generalization of classical minimal dominating set problem. Three algorithms
are proposed to approximate the minimum set of occupied nodes sufficient for
target observation. Extensive numerical results on computer-generated random
networks and real-world networks demonstrate that the proposed algorithms offer
superior performance in identification of a target minimal dominating set.
