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　α.　We　have　developed　an　approximation　algorithm　that　achieves　a　ratio　of　[Formula　presented].　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%.　©　2024　The　Author(s)