# Offloaded Computation for QoS Routing in Wireless Sensor Networks
## 4 Proposed Methodology
### Conflict-Free DODAG Construction (Algorithm 2)
#### 4.2.1 Redundancy Augmentation (Algorithm 3)  
After conflict-free DODAGs are constructed using Algorithm 2, routing robustness is enhanced by introducing _redundant links_. These links function as backup forwarding paths, thereby improving the fault tolerance and resilience of the network. Such links are particularly valuable for enabling the RPL local repair mechanisms, allowing recovery from transient failures without requiring global recomputation. Including redundant links is performed in a controlled manner that preserves adherence to the original QoS constraints, ensuring that the augmented DODAGs remain compliant with end-to-end requirements such as delay, reliability, and energy consumption.  
Algorithm 3 examines each node \(a\) in the DODAG and its adjacent neighbors \(b\). For each neighbor \(b\), a link \((a,b)\) is considered for addition if three conditions are met:  
1. Node \(b\) is part of the DODAG and its rank is not higher than that of node \(a\).
2. The aggregated QoS cost along the path from a leaf node to \(a\), the direct link \((a,b)\), and the path from \(b\) to the BR, denoted by \(\vec{L_{a}}+\vec{L_{a,b}}+\vec{L_{b}}\), satisfies the global QoS constraint \(\vec{L}\).
3. The resulting path structure remains acyclic and consistent with RPL directionality.  
Each successful insertion of a backup edge expands the routing graph without disrupting its primary hierarchical structure. This strategy ensures that nodes have alternative forwarding options in case of link failures, supporting improved reliability and load balancing during runtime.  
The network must be (re)configured either initially or when modifications occur, requiring a new set of DODAGs. The reconfiguration process involves removing outdated connections and establishing new ones. An effective reconfiguration should minimize disruption to ongoing communications with the BR and be executed as efficiently as possible. Prior research on reconfiguration processes for paths and trees, particularly multicast trees in optical networks, can be found in [60; 61].  
The reconfiguration generally follows a predefined schedule, where, at each step, a subset of nodes are updated. The list of nodes requiring reconfiguration (highlighted as gray nodes in Figure 4) is provided, while other nodes retain their original parent-child relationships in both the old and new DODAGs. In this example, we assume that node \(M\) can switch to an alternative parent \(F\), while nodes \(J\) and \(N\) can adopt \(H\) as their alternative parent. Additionally, the newly established paths from \(M\), \(J\), and \(N\) to the BR meet the required QoS constraints.  
A key feature of DODAG-based reconfiguration is that the new configuration automatically replaces the old one. During this process, existing traffic remains uninterrupted while new connections are established. The new DODAG is calculated by edge servers, ensuring that each covered node has a viable path. Throughout the reconfiguration, the previous version of the topology remains accessible on the server. Figure 4 illustrates the transition between the \(old\) and \(new\) topologies. As shown in the figure, a subset of nodes requires reconfiguration, while others retain their previous settings. The initial network setup is a special case in which all nodes need to undergo configuration.