Network slicing has appeared a key feature in 5G and beyond communication networks that enables the creation of multiple virtual networks (i.e., slices) over a shared physical network infrastructure. This process involves efficiently embedding (or mapping) each slice element, including virtual network functions (VNFs) and their interconnections, onto the physical network. This paper explores a scenario where the order of VNFs can be adjusted during slice embedding, offering greater flexibility to increase the number of services deployed on the infrastructure. We formulate a novel optimization framework to tackle the challenges of slice admission control and embedding with this flexibility. A heuristic is also introduced to derive embedding solutions in a timely manner. Simulation results demonstrate that allowing flexible VNF ordering significantly increases the number of slices that can be deployed in the network infrastructure.
