## 1 Introduction  
Network softwarization technologies such as Network Function Virtualization (NFV) and Software-Defined Networking (SDN) have enabled the provisioning of dynamic end-to-end services in 5G, Internet of Things, Industry 4.0, and other emerging trends. Traditionally, a service used to be a combination of various functions, statically deployed at a single or multiple locations. With NFV, functions in a service are separated and virtualized through Virtual Machines (VMs) or containers and are termed Virtual Network Functions (VNFs) or Service Functions (SFs). An orderly connected list of SFs, known as Service Function Chaining (SFC), delivers a specific service [1]. This not only enables operators to dynamically scale services, but also quickly provision new services by changing the order of SFs in SFC [2]. To satisfy the demand for uninterrupted high-quality services, in particular after the COVID-19 pandemic, the high availability of SFC is of paramount importance for operators under ever-increasing traffic load [3]. High availability for SFC requires an instant protection mechanism from the failure of network infrastructure (i.e., links, switches, servers) or software (i.e., VMs, containers). The protection mechanism for SFC stipulates that backup paths and SFs are installed at the initiation time of SFC. In the case of any failure event, the traffic is rerouted to the pre-installed backup path towards pre-deployed backup SFs. The protection mechanismsin conventional SDNs [4; 5] are not applicable to SFC, because the traffic in SFC needs to be routed through multiple intermediate destinations (i.e., SFs) in a given order before reaching the final destination. Additionally, the locations of backup SFs are not fixed as they are dynamically deployed after SFC creation depending on available resources and the proximity to the primary SFs. These SFC characteristics make the protection mechanism more complex than in conventional SDN. The protection of SFC consists of three sub-tasks: placement of backup SFs, decision regarding individual or shared backup SFs and their selection criteria, and proactive installation of backup paths and a traffic rerouting mechanism. Intuitively, the cost of backup path installation and end-to-end transmission delay become significant if the backup SFs are deployed at distant servers. On the contrary, the probability of the backup SFs' inaccessibility increases if they are placed in close proximity to their respective primary SFs. Most of the SFC recovery-related studies focused on this and increased SFC survivability by optimizing different parameters related to the placement of backup SFs [6; 7; 8]. Another concern related to the backup SFs' placement is the additional resource footprint, which is maximum in the case of a 1:1 mapping between primary and backup SFs. Sharing of backup SFs through M:N mapping between primary and backup SFs reduces the additional resource footprint, where M > N [9; 10]. These studies increased the network utilization and reduced end-to-end delay, but lacked a strategy for backup path setup with minimal installation cost and rerouting delay. Proactive installation of backup paths and a traffic rerouting mechanism for SFC protection seems trivial, but can result in high recovery delay and an increased number of control messages and flow entries, if not designed diligently. Approaches such as global and local protection from conventional networks either cause significant resource under-utilization or a critical increase in end-to-end transmission delays. This entails a backup path installation and traffic rerouting mechanisms (here onwards, the backup path installation and traffic rerouting mechanism are termed SFC protection for brevity),which benefit from the minimum end-to-end transmission delay and rapid recovery characteristics of global and local protection approaches, respectively, while avoiding their drawbacks.