Inter-switch networks for HPC systems and data-centers can be improved by applying random shortcut topologies with a reduced number of hops. With minimal routing in such networks; however, deadlock-freedom is not guaranteed. Multiple Virtual Channels (VCs) are efficiently used to avoid this problem. However, previous works do not provide good trade-offs between the number of required VCs and the time and memory complexities of an algorithm. In this work, a novel and fast algorithm, named ACRO, is proposed to endorse the arbitrary routing functions with deadlock-freedom, as well as consuming a small number of VCs. A heuristic approach to reduce VCs is achieved with a hash table, which improves the scalability of the algorithm compared with our previous work. Moreover, experimental results show that ACRO can reduce the average number of VCs by up to 63% when compared with a conventional algorithm that has the same time complexity. Furthermore, ACRO reduces the time complexity by a factor of O(|N|⋅log|N|), when compared with another conventional algorithm that requires almost the same number of VCs.