## 2 Related Works  
In contemporary times, the Internet is integral to people's daily lives, and network failures are a frequent occurrence. As a result, a multitude of solutions have been proposed to address these issues. This paper will discuss some of the routing protection algorithms that have been proposed to date. Routing protection algorithms [16; 17; 18] can be classified into two major types based on whether an auxiliary forwarding mechanism is required or not. In the category that does not require an auxiliary forwarding mechanism, there are various algorithms, such as Equal-Cost Multi-Path (ECMP) routing, Loop-Free Alternates (LFA), Node Protection Condition (NPC), U-turn, Downstream Rule (DC), JNHOR-SP, ESCAP, and Multi-path Routing with Available Paths (MARA). On the other hand, in the category that requires an auxiliary forwarding mechanism, there are Not-Via, tunnel-based routing protection algorithms, Segment Routing (SR), Multi-Configuration Routing (MRC), and Failure-carrying packet (FCP). These algorithms often necessitate additional mechanisms or devices to assist in forwarding traffic, ensuring a quick switch to backup paths in case of failure on the primary path. The primary objective of the routing protection algorithm is to compute a loop-free backup path for each node within the network. This ensures that communication can be swiftly rerouted to the backup path if the optimal path fails, thereby guaranteeing uninterrupted communication. The Downstream Criterion (DC) [19] is a prevalent loop-free calculation method employed in network protection. This approach enhances fault recovery efficiency by ensuring that the backup path is as close as possible to the main path in terms of physical location within the network. The MARA algorithm [20] fundamentally transforms the network topology into a directed acyclic graph (DAG). This transformation ensures that each link in the network has a unidirectional orientation. A notable characteristic of the DAG is the unidirectionality of its links, which impacts the node's ability to compute loop-free backup next hops by limiting their possibilities. Furthermore, the efficiency of the MARA algorithm is intrinsically tied to the network topology, influencing its failure protection rate. In contrast, the bidirectional nature of the Joker link [21] enables more effective traffic rerouting upon failure. Yet, the JNHOR-SP algorithm's average failure protection rate is only approximately 95%, suggesting potential for enhancement despite leveraging the Joker link. The LFID (loop-free import-dependent) algorithm [22] offers a different approach, focusing on loop-free routing based on packet incoming port. This strategy augments redundant paths in the DAG, bolstering the network's failure recovery capability. However, akin to the JNHOR-SP algorithm, its failure protection rate remains suboptimal, fluctuating between 88.9% and 98.2%. The literature [23] leverages Not-Via addresses to facilitate swift responses to network failures. In the presence of faulty nodes or links, the Not-Via address directs packets to circumvent these problematic areas. This approach enhances rerouting efficiency by using address selection to guide packet forwarding. The ESCAP [24] algorithm is specifically designed to safeguard against single node failures in the network. However, a notable limitation of this algorithm is its disregard for the cost of the path when calculating backup nodes. This oversight can lead to an increased Path Stretching Degree for the algorithm; in the event of a failure, packets may be rerouted along longer, potentially non-optimal paths. This issue with the Path Stretching Degree can significantly impact the performance of the network, particularly in congested networks or applications that necessitate low latency communication. The Multi Routing Config (MRC) [25] algorithm is adept at computing multiple configuration graphs by dynamically adjusting link costs within the network.