# A Game Model and Fault Recovery Algorithm for SDN Multi-Domain
## 2 Related Work  
The control plane is the most vulnerable component of the entire network, and the layout of controllers affects aspects such as network delay, energy efficiency, load, and network resilience, which has garnered significant attention from researchers. Currently, research on the reliability technology of the control plane in SDN architectures primarily focuses on controller deployment, fault detection, and fault recovery. Scholars have modeled and analyzed the Controller Placement Problem (CPP) in SDN based on graph theory, game theory, queuing theory, etc. For example, [PERSON] et al. [8] suggested that, based on the meta-heuristic algorithm, the discrete African Vulture optimization algorithm (AVOA) was solved by low-complexity multi-point and two-point permutation methods in the search stage and the development stage to optimize the controller placement scheme. [PERSON], et al. [9] proposed to prevent the significant increase in worst-case delay and disconnection by predicting failures so as to minimize the worst-case delay between the switch and its backup controller, as well as between controllers. Current research on the CPP mainly involves three objectives: minimizing network delay and controller deployment costs and maximizing network reliability. [PERSON] proposed an improved K-means algorithm based on an artificial bee colony (ABCK) [10] to efficiently calculate the optimal or near-optimal solutions. To minimize propagation delays between controllers and switches and maintain load balance between controllers. [PERSON] et al. put forward a highly reliable, delay-optimized controller placement (HR-DO) algorithm [11], which can be used to optimize the number of controllers required in a network and reduce network delay. It also improves the reliability and robustness of SDN while minimizing the delay in the worst-case scenario. [PERSON] et al. raised an optimization model [12] to jointly upgrade the placement of primary and standby controllers in long-distance SDN networks, which can enhance the elasticity and dependability of the network against node attacks. [PERSON] proposed a multi-controller placement strategy based on the improved [PERSON] optimization algorithm [13]. Considering the total network delay, node reliability, link failure rate, and total placement cost, the switching mode of dynamic adaptive global search and local search can enhance the diversity of CPP schemes and improve placement reliability. Network deployment cost and energy consumption are also important factors affecting control plane reliability. Solutions to minimize controller deployment costs can be summarized as static and dynamic methods. Static methods take into account the optimal number, type, location of controllers, and interconnection information between switches and controllers. [PERSON] et al. considered the control plane and IoT traffic and proposed an energy-saving controller placement scheme, EnPlace [14]. Compared to existing solutions, EnPlace can significantly save energy. [PERSON] et al. focused on studying energy-efficient routing mechanisms for traffic in SDN-based operator Ethernet networks. A heuristic algorithm [15] is put forward to select the switches and links to be disabled according to predefined criteria. Taking the constraint of link capacity into consideration, existing traffic is rerouted through the best available path. Relevant scholars have studied the fault recovery of controllers in SDN distributed architectures from controller placement and migration of out-of-control switches. One research focus is on controller deployment and optimization, where the network is abstracted as an undirected topology graph, and the controller deployment can be regarded as a partition mapping problem for the topology. Under the existing network topology, controllers need to comprehensively consider the impact of inter-device hops and propagation delays. The selection of controller locations is determined by the positions of switch nodes.