Internet of Things is one of the most promising domain for developing new and smart applications. For some applications, Quality of Service requirement may be imposed. However, the things connected in this kind of networks are often vulnerable and dotted by limited energy (Low-power and Lossy Networks, LLNs). These networks need special solutions for routing and RPL is a standard IPv6 routing protocol to respond to needs. RPL build Destination Oriented Directed Acyclic Graphs (DODAGs) for routing. Recently, some propositions have been formulated to satisfy QoS requirements in LLNs using RPL even if there are several QoS constraints. A greedy DODAG construction has been proposed based on a Non-Linear Length which takes into account any number of constraints for QoS routing. However, it is known that the multi-constrained QoS routing is an NP-hard problem and its solution is not always a simple acyclic graph (not a tree). In this paper we present the computation of the exact solution in LLNs between a Border Router and the nodes respecting a set of QoS constraints. We propose the modification of RPL for this. Our analysis also covers a set of parameterized polynomial algorithms. We evaluate the performance of the proposed algorithms in term of execution time and scalability, the number of missing nodes during the construction of the DODAG and the quality of the paths from the Border Router to each node in the constructed DODAG.