# Offloaded Computation for QoS Routing in Wireless Sensor Networks
## 1 Introduction
### Main Contributions  
Although many RPL-based QoS routing extensions have been proposed in recent years [5; 6; 7], a critical **research gap** persists: most solutions either rely on modifying the RPL objective functions [8; 9], adopt loosely coupled metric composition techniques that reduce transparency and control [10], or lack the computational scalability necessary to efficiently handle multiple concurrent QoS constraints [7; 11]. Furthermore, very few approaches leverage edge computing to offload the path computation workload in a centralized and conflict-resilient manner. This research targets QoS-aware routing in Wireless Sensor Networks (WSNs), where the goal is to find routes that satisfy multiple QoS constraints simultaneously. Whenmultiple QoS criteria are involved, the problem becomes a Multi-Constrained Optimal Path (MCOP) problem, known to be NP-complete. Traditional approaches often require significant computational resources and do not guarantee a feasible solution, even when one exists. The Routing Protocol for Low-Power and Lossy Networks (RPL) [12] is the de facto standard for routing in WSNs. However, incorporating multi-constrained QoS support within the RPL remains challenging due to the increased processing complexity and associated control overhead. The existing RPL extensions often trade scalability for QoS-awareness or compromise protocol compatibility by modifying objective functions. To address these challenges, our work proposes a scalable, modular, and standard-compliant architecture that enables QoS-aware routing without altering the RPL internal mechanisms. The main contributions are summarized as follows:  
1. **A formal problem formulation** that defines multi-constrained QoS routing in WSNs as an NP-complete MC(O)P problem and contextualizes its integration challenges within the structural and computational limitations of the RPL. 2. **A centralized QoS route computation algorithm** that computes multiple feasible and non-dominated paths while _preserving full compliance with RPL objective functions_[5; 12; 13], enabling seamless deployment over standard-compliant networks. 3. **An edge offloading architecture** that delegates path computation and DODAG construction to external servers [2; 14; 15], significantly reducing the processing burden on constrained sensor nodes. This design contrasts with prior in-network QoS routing approaches [16; 17] and aligns with the recent trends in computation offloading to external infrastructures for enhanced QoS, as also explored in hybrid satellite networks [18]. 4. **A lightweight conflict detection and redundancy augmentation mechanism** that builds robust loop-free DODAGs under QoS constraints without increasing control overhead. This avoids the complexity of previous extensions that depend on metric redefinition or extensive signaling [9; 10]. 5. **Comprehensive performance evaluation** under varying network sizes, QoS constraint profiles, and BR placements. The results show that the proposed approach preserves between _143% and 1282% more QoS-satisfying nodes_ compared to the heuristic- and composition-based baselines, with an average improvement of over 560%, validating its scalability and robustness under strict multi-constraint conditions. 6. **New insights into QoS routing dynamics in WSNs**, including how the number of QoS constraints, path feasibility rates, and route lengths interact. These findings offer practical guidelines for QoS-aware WSN planning and deployment. To substantiate the novelty of the proposed work, Table 1 provides a comparative analysis with selected representative works. The comparison highlights the distinctive features of our approach in terms of protocol compliance, control overhead minimization, and support for lightweight, conflict-free, and redundant path construction. The remainder of this paper is structured as follows: Section 2 reviews the related work. Section 3 introduces our model for multi-constrained path computation and its key challenges.