Wireless sensor networks (WSNs) may be deployed in failure-prone environments, and WSNs nodes easily fail due to unreliable wireless connections, malicious attacks and resource-constrained features. Nevertheless, if WSNs can tolerate at most losing k - 1 nodes while the rest of nodes remain connected, the network is called k - connected. k is one of the most important indicators for WSNs’ self-healing capability. Following a WSN design flow, this paper surveys resilience issues from the topology control and multi-path routing point of view. This paper provides a discussion on transmission and failure models, which have an important impact on research results. Afterwards, this paper reviews theoretical results and representative topology control approaches to guarantee WSNs to be k - connected at three different network deployment stages: pre-deployment, post-deployment and re-deployment. Multi-path routing protocols are discussed, and many NP-complete or NP-hard problems regarding topology control are identified. The challenging open issues are discussed at the end. This paper can serve as a guideline to design resilient WSNs.

Topology control is an important technique to improve the connectivity and the reliability of Wireless Sensor Networks (WSNs) by means of adjusting the communication range of wireless sensor nodes. In this paper, a novel Fuzzy-logic Topology Control (FTC) is proposed to achieve any desired average node degree by adaptively changing communication range, thus improving the network connectivity, which is the main target of FTC. FTC is a fully localized control algorithm, and does not rely on location information of neighbors. Instead of designing membership functions and if-then rules for fuzzy-logic controller, FTC is constructed from the training data set to facilitate the design process. FTC is proved to be accurate, stable and has short settling time. In order to compare it with other representative localized algorithms (NONE, FLSS, k-Neighbor and LTRT), FTC is evaluated through extensive simulations. The simulation results show that: firstly, similar to k-Neighbor algorithm, FTC is the best to achieve the desired average node degree as node density varies; secondly, FTC is comparable to FLSS and k-Neighbor in terms of energy-efficiency, but is better than LTRT and NONE; thirdly, FTC has the lowest average maximum communication range than other algorithms, which indicates that the most energy-consuming node in the network consumes the lowest power.

Wireless sensor networks (WSNs) consist of thousands of nodes that need to communicate with each other. However, it is possible that some nodes are isolated from other nodes due to limited communication range. This paper focuses on the influence of communication range on the probability that all nodes are connected under two conditions, respectively: (1) all nodes have the same communication range, and (2) communication range of each node is a random variable. In the former case, this work proves that, for , if the probability of the network being connected is , by means of increasing communication range by constant , the probability of network being connected is at least . Explicit function is given. It turns out that, once the network is connected, it also makes the WSNs resilient against nodes failure. In the latter case, this paper proposes that the network connection probability is modeled as Cox process. The change of network connection probability with respect to distribution parameters and resilience performance is presented. Finally, a method to decide the distribution parameters of node communication range in order to satisfy a given network connection probability is developed.

The sensor nodes in the Wireless Sensor Networks (WSNs) are prone to failures due to many reasons, for example, running out of battery or harsh environment deployment; therefore, the WSNs are expected to be able to maintain network connectivity and tolerate certain amount of node failures. By applying fuzzy‐logic approach to control the network topology, this paper aims at improving the network connectivity and fault‐tolerant capability in response to node failures, while taking into account that the control approach has to be localized and energy efficient. Two fuzzy controllers are proposed in this paper: one is Learning‐based Fuzzy‐logic Topology Control (LFTC), of which the fuzzy controller is learnt from a training data set; another one is Rules‐based Fuzzy‐logic Topology Control (RFTC), of which the fuzzy controller is obtained through designing if‐then rules and membership functions. Both LFTC and RFTC do not rely on location information, and they are localized. Comparing them with other three representative algorithms (LTRT, List‐based, and NONE) through extensive simulations, our two proposed fuzzy controllers have been proved to be very energy efficient to achieve desired node degree and improve the network connectivity when sensor nodes run out of battery or are subject to random attacks.