This paper addresses the problem of maintaining sensing coverage and connectivity in large wireless sensor networks by minimizing the number of active sensor nodes. The authors investigate the relationship between coverage and connectivity, proving that if the radio range is at least twice the sensing range, complete coverage of a convex area implies connectivity. This allows the focus to shift to the coverage problem. Under the assumption of high node density, they derive optimality conditions for full coverage. Based on these conditions, they propose a decentralized and localized density control algorithm called Optimal Geographical Density Control (OGDC). Simulation results show that OGDC outperforms existing algorithms in terms of the number of active nodes needed and achieves similar coverage performance. The paper discusses the challenges of maintaining coverage and connectivity in high-density sensor networks, where energy conservation is critical. It highlights the importance of density control to ensure that only a subset of nodes operate in the active mode while maintaining coverage and connectivity. The authors also emphasize the need for a distributed and localized algorithm to manage sensor networks effectively. The paper presents a detailed analysis of the relationship between coverage and connectivity, proving that under certain conditions, coverage implies connectivity. It then derives optimality conditions for full coverage under ideal node density assumptions. Based on these conditions, the authors propose OGDC, a decentralized and localized algorithm for density control. The algorithm is validated through simulations, which show that OGDC outperforms existing algorithms in terms of the number of active nodes needed and achieves similar coverage performance. The paper also discusses related work, including existing algorithms for sensing coverage and connectivity in sensor networks. It highlights the limitations of these algorithms and the importance of addressing both coverage and connectivity in sensor networks. The authors conclude that their approach provides a more efficient and effective solution for maintaining coverage and connectivity in large sensor networks.This paper addresses the problem of maintaining sensing coverage and connectivity in large wireless sensor networks by minimizing the number of active sensor nodes. The authors investigate the relationship between coverage and connectivity, proving that if the radio range is at least twice the sensing range, complete coverage of a convex area implies connectivity. This allows the focus to shift to the coverage problem. Under the assumption of high node density, they derive optimality conditions for full coverage. Based on these conditions, they propose a decentralized and localized density control algorithm called Optimal Geographical Density Control (OGDC). Simulation results show that OGDC outperforms existing algorithms in terms of the number of active nodes needed and achieves similar coverage performance. The paper discusses the challenges of maintaining coverage and connectivity in high-density sensor networks, where energy conservation is critical. It highlights the importance of density control to ensure that only a subset of nodes operate in the active mode while maintaining coverage and connectivity. The authors also emphasize the need for a distributed and localized algorithm to manage sensor networks effectively. The paper presents a detailed analysis of the relationship between coverage and connectivity, proving that under certain conditions, coverage implies connectivity. It then derives optimality conditions for full coverage under ideal node density assumptions. Based on these conditions, the authors propose OGDC, a decentralized and localized algorithm for density control. The algorithm is validated through simulations, which show that OGDC outperforms existing algorithms in terms of the number of active nodes needed and achieves similar coverage performance. The paper also discusses related work, including existing algorithms for sensing coverage and connectivity in sensor networks. It highlights the limitations of these algorithms and the importance of addressing both coverage and connectivity in sensor networks. The authors conclude that their approach provides a more efficient and effective solution for maintaining coverage and connectivity in large sensor networks.