## 2 Related Work  
There are two types of relay node placement strategies for EH-WSNs, namely, constrained and unconstrained approaches. The constrained approach sets specific objectives, namely, enhancing the network life, improving the coverage, and specific location restrictions, etc. The unconstrained approach for relay node placement focuses on generalized objectives such as connectivity and fault tolerance in EH-WSN. We will first discuss the unconstrained strategies for relay node placement. The objective of fault tolerance in single-tiered (ST) as well as two-tiered (TT) EH-WSNs can be achieved by providing k-connectivity with k \(\geq\) 2. Further, if k = 1, then ultimate objective is internode reachability, with a focus on generating fully connected EH-WSN. Next, [PERSON] et al. [17] have presented an M1 tRNP scheme, which is known as the minimum 1-tiered relay node placement scheme. For single-tiered (ST), the proposed scheme utilized polynomial-time 7-approximation and on the other hand for two-tiered networks, 5 + \(\varepsilon\) (\(\varepsilon\) > 0). Here, [PERSON]'s algorithm is used for constructing the MST. The sensing radius of the relay nodes is utilized for placing the RNs on the edges of the tree. [PERSON] et al. [18] proposed an approximation framework for one connected network with polynomial time (6 + \(\varepsilon\)) and two connected networks with (24 + \(\varepsilon\)). The Steiner minimum tree is utilized for determining the minimum number of RNs, covering the entire set of SNs for one connected network. Next, the scheme is further extended for two connected networks; here, extra relay nodes are deployed for each relay node in one connected network. Next, we will discuss the constrained strategies for relay node placement. [PERSON] et al. [19] have addressed the objective of reducing the cost of a network with improvement in network life span. This problem is NP-hard, also known as the minimum set covering problem. In the proposed recursive scheme, the divide and conquer strategy is utilized. In the proposed scheme, the relay nodes are deployed in the locations where the SNs' ranges intersect. In [19], the focus is on deploying the minimum number of relay nodes for a two-tiered architecture with the objective of achieving the load balancing. The locations are identified where ranges of relay nodes intersect for extra relay node deployment and the focus is on achieving k-connectivity. Next, there are four classifications of relay node optimization strategies, namely, algorithm-based frameworks, approximation algorithm-based frameworks, frameworks based on heuristics, and frameworks based on metaheuristics. We will illustrate each strategy one by one starting from algorithm-based frameworks. [PERSON] et al. [20] have proposed two efficient frameworks for the positioning of the distributed RNs. These two frameworks are aimed at reducing the cost of movement of the RNs for guaranteed recovery of the network. The first proposed framework focused on the movements of RNs based on virtual force on the other hand the second proposed framework utilized the concept of Game Theory among the partitions of the network. Next, [PERSON] et al. [21] have proposed an efficient framework for jigsaw-based placement of RNs for indoor WSNs. They aimed at constructing the WSNs, with the minimum number of RNs and SNs in an indoor space with obstructions. Further, [PERSON] et al. [22] have proposed an enhanced framework for the placement of RNs. They aimed at optimizing the overall cost by utilizing the least possible RNs. The enhanced framework ensures optimal k-coverage and s-connectivity with respect to SNs and RNs within the network. The next paragraph will illustrate the approximation algorithm-based frameworks for relay node optimization. [PERSON] et al. [23] have conducted extensive studies for the constrained RN placement problem (CRNPP) with prior knowledge for candidate locations regarding the potential of energy harvesting.