## 3 Related Work  
### Connectivity Restoration  
The issue of fault tolerance in different contexts for WSANs has only been studied in few publications. For instance, the fault-tolerant model presented in [9] assigns multiple actors to each sensor and multiple sensors to each actor in order to ensure guaranteed event notification, even in cases of either failure or inaccessibility. However, our fault-tolerant model operates in the context of maintaining inter-actor connectivity rather than reliable sensor-actor communication. Few researchers have exploited node mobility as a means for performance optimization both in sensor networks and WSANs. However, exploiting node mobility to mend severed topologies has just recently started to attract attention. The reader is referred to [10] for a comprehensive survey of node relocation strategies.  
The existing work can be categorized into block and cascaded movement. Block movement often requires a high pre-failure connectivity in order for the nodes to coordinate their response. An example of block movement based approaches is reported in [11], where the initial network is assumed to be 2-connected and goal is to sustain such 2-connectivity even under link or node failure. The idea of movement of robots is similar to ours but their approach requires a centralized algorithm. [PERSON] _et al._ presented a distributed approach to the similar problem that strives to restore 2-connectivity in [12]. Unlike [11] and [12], our algorithm focuses on providing 1-connectivity.  
Block movements often become infeasible in the absence of a higher level of connectivity. Therefore, few researchers have pursued cascaded node movement that can be further categorized based on network state information that nodes are assumed to maintain. Some approaches like DARA [2], or PADRA [13] require each actor to maintain 2-hop neighbors. Others, such as RIM [3], C\({}^{3}\)R [4], and VCR [5] avoid the increased overhead for tracking 2-hop neighbors and require each node to maintain only its directly reachable nodes, _i.e._, 1-hop neighbors. Like our proposed PCR algorithm, DARA strives to restore connectivity lost due to cut-vertex failures. However, DARA requires more network state in order to ensure convergence. Meanwhile, in PADRA, [PERSON] _et al._ identify a connected dominating set (CDS) of the whole network in order to detect cut-vertices. Since the CDS based method is not accurate for critical node detection, they perform a depth-first search (DFS) on each member for the CDS to confirm whether that the node is really a cut vertex or not. Although, they use a distributed algorithm their solution still requires 2-hop neighbors' information that increases messaging overhead. Another work proposed in [14] also uses 2-hop information to detect cut-vertices. The proposed PCR algorithm relies only on 1-hop information and reduces the communication overhead. Although RIM, C\({}^{3}\)R and VCR use 1-hop neighbor information to restore connectivity, they are purely reactive and do not differentiate between critical and non-critical nodes, whereas, PCR is a hybrid algorithm that proactively identifies critical nodes and designates them an appropriate backup that is responsible for restoring lost connectivity.