This is the accepted version of a paper published in IEEE Communications Surveys and Tutorials. This paper has been peer-reviewed but does not include the final publisher proofcorrections or journal pagination.

The recent development of low cost wireless sensors enables novel Internet-of-Things (IoT) applications, such as the monitoring of water distribution networks. In such scenarios, the lifetime of the wireless sensor network (WSN) is a major concern, given that sensor node replacement is generally inconvenient and costly. In this paper, a compressive sensing based scheduling scheme is proposed that conserves energy by activating only a small subset of sensor nodes in each timeslot to sense and transmit. Compressive sensing introduces a cardinality constraint that makes the scheduling optimization problem particularly challenging. Taking advantage of the network topology imposed by the IoT water monitoring scenario, the scheduling problem is decomposed into simpler subproblems, and a dynamicprogramming-based solution method is proposed. Based on the proposed method, a solution algorithm is derived, whose complexity and energy-wise performance are investigated. The complexity of the proposed algorithm is characterized and its performance is evaluated numerically via an IoT emulator of water distribution networks. The analytical and numerical results show that the proposed algorithm outperforms state-of-the-art approaches in terms of energy consumption, network lifetime, and robustness to sensor node failures. It is argued that the derived solution approach is general and it can be potentially applied to more IoT scenarios such as WSN scheduling in smart cities and intelligent transport systems.Index Terms-Energy balancing, energy efficiency, water distribution networks, compressive sensing 0733-8716 (c)

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Abstract-Many physical systems, such as water/electricity distribution networks, are monitored by battery-powered Wireless Sensor Networks (WSNs). Since battery replacement of sensor nodes is generally difficult, long-term monitoring can be only achieved if the operation of the WSN nodes contributes to a long WSN lifetime. Two prominent techniques to long WSN lifetime are i) optimal sensor activation and ii) efficient data gathering and forwarding based on compressive sensing. These techniques are feasible only if the activated sensor nodes establish a connected communication network (connectivity constraint), and satisfy a compressive sensing decoding constraint (cardinality constraint). These two constraints make the problem of maximizing network lifetime via sensor node activation and compressive sensing NP-hard. To overcome this difficulty, an alternative approach that iteratively solves energy balancing problems is proposed. However, understanding whether maximizing network lifetime and energy balancing problems are aligned objectives is a fundamental open issue. The analysis reveals that the two optimization problems give different solutions, but the difference between the lifetime achieved by the energy balancing approach and the maximum lifetime is small when the initial energy at sensor nodes is significantly larger than the energy consumed for a single transmission. The lifetime achieved by the energy balancing is asymptotically optimal, and that the achievable network lifetime is at least 50% of the optimum. Analysis and numerical simulations quantify the efficiency of the proposed energy balancing approach.