H-hop independently submodular maximization problem with curvature

The Connected Sensor Problem (CSP) presents a prevalent challenge in the realms of communication and Internet of Things (IoT) applications. Its primary aim is to maximize the coverage of users while maintaining connectivity among K sensors. Addressing the challenge of managing a large user base alongside a finite number of candidate locations, this paper proposes an extension to the CSP: the h-hop independently submodular maximization problem characterized by curvature $\alpha$. We have developed an approximation algorithm that achieves a ratio of $\frac{1-e^{-\alpha }}{(2h+3)\alpha }$. The efficacy of this algorithm is demonstrated on the CSP, where it shows superior performance over existing algorithms, marked by an average enhancement of 8.4%.