Distributed routing methods with small routing tables are scalable design on irregular networks for large-scale High Performance Computing (HPC) systems. Recently proposed compact routing methods, however, do not guarantee deadlock-freedom. Cyclic channel dependencies on arbitrary routing are typically removed with multiple Virtual Channels (VCs). However, challenges still remain to provide good trade-offs between a number of required VCs and a time complexity of an algorithm for assignment of VCs to paths. In this work, a novel algorithm ACRO is proposed for enriching arbitrary routing functions with deadlock-freedom with a reasonable number of VCs and a time complexity. Experimental results show that ACRO can reduce the average number of required VCs by up to 63% compared with the conventional algorithm that has the same time complexity. Furthermore, ACRO reduces a time complexity by a factor of O(|N| · log|N|) compared with that of the other conventional algorithm that needs almost the same number of VCs.