## 8 Conclusions  
This paper surveys resilience issues in WSNs from the topology control and multi-path routing point of view. In general, the key to keeping the network resilient against failures is to maintain the network as \(k-connected\), where \(k\) is the most important indicator for resilience. The conclusions in this survey are the following:  
(1) The first step to study the resilience issue is to employ the network models and failure models. This work shows that the network model is quite complicated. To fully capture the most important features of sensor nodes, one should adopt more realistic models and avoid using ideal models. We believe that the most commonly-used models, such as a homogeneous network and a regular radio model, are inappropriate to model WSNs. (2) In order to improve the resilience of WSNs, many approaches can act on three different deployment stages to improve the connectivity. At the pre-deployment stage, in the case that the nodes are randomly deployed, the theoretical result shows what is the condition to have the network \(k-connected\) with high probability; in the case that the node location can be controlled, the required \(k-connected\) network can be constructed. At the post-deployment stage, the main methods are controlling the transmission range (power) or scheduling the node status to achieve the desired connectivity or link quality. In the re-deployment stage, WSNs can maintain or improve connectivity by placing new relay nodes. By doing this, this paper provides a framework that can help researchers design resilient WSNs at different stages. (3) Once the network is deployed, multi-path routing can be used to establish resilient paths from the source to the destination. (4) It turns out that many issues related to WSNs' resilience are very challenging; they are either NP-complete or NP-hard problems. Therefore, optimal solutions do not exist. This paper identifiesthose problems and points out that those most proposed algorithms are still centralized. It is expected that more distributed heuristic algorithms will be proposed in the future. (5) In most cases, the \(k-connected\) network is not the only goal desired; other goals, such as energy efficiency, coverage and the number of nodes deployed, are also need to be taken into account when designing resilient WSNs. (6) Considering the \(3-dimensions\) and mobile network model in the study of resilient WSNs may be interesting. (7) Although the \(1-connected\) topologies are not able to tolerate node failures (such as chain topology and tree-based topologies), one can construct a fault-tolerant network, e.g., \(k-connected\) network (\(k>1\)), by using many \(1-connected\) networks. (8) Finally, this paper found that a great part of the literature is dedicated to solving the \(k-connected\) problem for only one deployment stage. It is possible and necessary that those approaches at different deployment stages can be integrated to maximize the fault tolerance capability. For instance, at the pre-deployment stage, the initial network should be built to be \(k-connected\) with high \(k\); at the post-deployment stage, the transmission range to maintain a \(k-connected\) network should be controlled; if node failures occur so that it is impossible to maintain a network \(k-connected\), the approaches that calculate the locations for new nodes to recover connectivity can be used. This survey intends to provide researchers the state-of-the-art solutions concerning resiliency issues in WSNs at different design stages. A novel perspective on designing resilient WSNs is provided, as well. In order to do this, we clarified the concept of resilience and offered clear guidelines on the appropriate models that should be considered, as well as in which stage(s) the techniques can be applied, and we identified the problems that are still very challenging. Thus, this paper can serve as a guideline for the design of resilient WSNs. Currently, we are developing a real sensor network using our proposed topology control systems.