# Survivable Deployments of Optical Sensor Networks against Multiple Failures and Disasters: A Survey
## 2 Existing Survivability Technologies in OSNs
### Pre-Configured Protection Schemes
#### 2.3.4 The Pre-Configured K-Regular and K-(Edge)-Connected (K&K) Structure Scheme  
Although the p-cycle scheme can be used to achieve multi-failure protection, it consumes too many spectrum resources. There is a pressing need to find a new protection structure that has higher spectrum efficiency and lower resource redundancy against multiple failures. In theory, p-cycle is the optimal protection structure against single failure. P-cycle is a two-regular and two-connected structure. Based on this, the pre-configured K&K structures to achieve multi-failure protection were proposed. It can be proved that the pre-configured K&K structure was the optimal protection structure against multiple failures. As presented in Figure 6, two p-cubes were designed for dual-link failures. When two failures occurred on any two links, the interrupted working flow could be restored by the two cubes. The pre-configured K&K was researched in WDM networks and elastic optical networks. In [98], the authors proposed K&K structures for providing protection against multiple failures in optical transport networks. In [99], the authors applied K&K structures to ultra-high capacity optical networks. They conducted theoretical analyses and showed that pre-configured K&K structures could reach the lower bound of logical redundancy. In [100], the authors presented an OpenFlow-based K&K structure configuration mechanism for elastic optical networks against concurrent multi-faults. In [101; 102], a preconfigured \(k\)-edge-connected structure (p-kces) was proposed in WDM networks. Many preconfigured protection structures have been proposed based on the pre-configured K&K structure, such as a pre-configured polyhedron (p-poly) structure, pre-configured multi-dimensional protection (p-MDP) structure, p-cube structure, preconfigured ball (p-ball) structure, and pre-configured prism structure.  
**P-Poly Structure**: P-poly is a kind of pre-configured K&K structure. In [103], the authors proposed a novel protection scheme based on a p-poly structure against multi-link failures in high capacity and large-scale optical transport networks. In [104], the authors developed an efficient ILP construction model and two resource allocation schemes for p-poly.  
**P-MDP Structure**: The P-MDP structure was proposed to resist multi-link failures. In [105], the authors proposed a pre-configured multi-dimensional protection (p-MDP) structure against simultaneous m-link failures in high capacity and large-scale optical transport networks. In [106], a k-dimensional protection structure (KDPS) was proposed against k - 1 failures. Two greedy algorithms were proposed to construct KDPS in static and dynamic optical networks, respectively.  
**P-Cube/P-Ball/P-Prism Structures**: The p-cube/p-ball/p-prism structures were proposed to resist dual-link failures. In [107], the authors proposed the p-cube structure in multi-dimensional node-based optical networks. Compared with p-cycle, p-cube fully used the node connectivity topology to employ fewer protection links against simultaneous dual-link failures. In [108], the authors proposed p-cube to deal with multi-link failures in a server-centric data center. The results showed that p-cube had better performance than p-cycle at the resource utilization rate and protection rate. In [109], the authors proposed a p-ball protection method for dual-link failures in optical mesh networks. The p-ball protection was better in terms of both construction cost metrics and operation cost metrics (such as average hop and protection resource utilization ratio). In [110], the authors proposed the p-prism structure against simultaneous dual-link failure and proved that it used less protection links than p-cycle.