Adaptive influence maximization is an important research problem in computational social networks, which is also a typical problem in the study of adaptive processing of information and adaptive construction of objects. In this paper, we propose a new method that reduces the adaptive influence maximization problem into a nonadaptive one in a different social network, so that an adaptive optimization can be solved by those methods for nonadaptive optimization. In addition, we provide a new approximation algorithm for the submodular maximization problem with a knapsack constraint, which runs in [Formula: see text] time and has performance ratio [Formula: see text], where n is the number of nodes in the network. The ratio is better than the best known previous one with the same running time. History: Accepted by Erwin Pesch, Area Editor for Heuristic Search & Approximation Algorithms. Funding: This research is supported in part by the National Natural Science Foundation of China [Grant U20A2068].

In wireless sensor network, each sensor can monitor an area, which is a disk with center at the sensor. Considering a set of sensors and given a target area, how do we select a subset of sensors to monitor the target area?Note that a whole area is monitored (or say covered) if every point in the area is covered. We cannot check at every point. Usually, one selects a set of points in the target area, called target points, such that the target area is covered by a subset of sensors if and only if all target points are covered.The question is how many target points can replace a target area in such a way? The existing method needs O(n2) target points when n sensors are considered. In this paper, we propose a method to reduce this number. This would improve the performance of wireless sensor networks.