# Offloaded Computation for QoS Routing in Wireless Sensor Networks
## 2 Related Work
### QoS Extensions to RPL  
The RPL (Routing Protocol for Low-Power and Lossy Networks) is a standardized protocol designed to establish a multi-hop tree-based mesh topology over networks characterized by lossy links. Its primary objective is to facilitate data delivery from source nodes, such as sensors, to sink nodes or BRs. This protocol, which operates within the framework of IPv6, employs a distributed route construction mechanism overseen by an objective function (OF), tasked with selecting the optimal links for route mapping. Nevertheless, the RPL is susceptible to challenges related to mobility and reliability.  
The routing architecture employed in the RPL is structured as a Destination-Oriented Directed Acyclic Graph (DODAG). An effective and adaptive link quality estimation (LQE) is crucial for selecting the optimal routing paths, especially under dynamic network conditions. Research by [PERSON] et al. [45] presented a link quality estimation method that leverages reinforcement learning techniques. Additionally, [PERSON] et al. [17] introduced a novel objective function and two heuristic routing algorithms that adhere to QoS constraints for multi-constrained QoS routing within Low-Power and Lossy Networks (LLNs). Their approach accommodates constraints and metrics for QoS routing, allowing for non-linear path lengths.  
**Definition 1** (Non-linear length).: _Let \(w(e)\) be the vector of \(K\) values of QoS parameters in the edge \(e\) and \(\vec{L}\) be the vector of the \(K\)-tolerated end-to-end values for any QoS paths. The non-linear length of a path \(P\) is a scalar_  
\[w_{NL}(P)=\max_{i=1,\ldots,K}\frac{\sum_{e\in P}w_{i}(e)}{L_{i}}\]  
In a related study by [PERSON] et al. [46], an auxiliary edge weight was computed as \(w_{a}(e)=\max_{i=1,\ldots,K}\frac{w_{i}(e)}{W}\) for each edge \(e\) using a constant value \(W\). The authors suggested that this constant could be replaced with an application-specific value \(L_{i}\), providing a \"projection\" of the non-linear length onto the edge. The shortest path can then be determined using this auxiliary weight to identify QoS-compliant routes.  
Furthermore, a method compatible with the RPL that incorporates non-linear length considerations was proposed by [PERSON] et al. [17]. Within the DODAG construction process, each node is expected to retain a weight vector computed from the sink to itself. The preferred parent node among neighbors is identified as the one that offers the minimal non-linear path length for the given node, and this selection is communicated to the neighboring nodes. This algorithm links all the nodes within the subtree, rooted at the respective node, along the same path, although this may not always yield feasible solutions for certain nodes.  
[PERSON] et al. [17] discussed modifications to determine the optimal paths for all nodes, striving for an ideal solution. These modifications involve a decision-making mechanism that allows nodes sufficient time to gather alternative paths from potential parent and child nodes. This strategy ensures that comprehensive information is available to inform optimal decision-making. It is important to note that this solution demands considerable computational resources and may introduce significant delays in the system's response.  
Additional modifications are suggested, including limiting the number of analyzed paths to a specified integer value \(k\), which aligns with the computational approachesoutlined in [47]. The findings indicate that exact route computations may not be advisable given the resource constraints inherent in LLNs.