Optimization of MPI collective communication operations has been an active research topic since the advent of MPI in 1990s. Many general and architecture-specific collective algorithms have been proposed and implemented in the state-of-the-art MPI implementations. Hierarchical topology-oblivious transformation of existing communication algorithms has been recently proposed as a new promising approach to optimization of MPI collective communication algorithms and MPI-based applications. This approach has been successfully applied to the most popular parallel matrix multiplication algorithm, SUMMA, and the state-of-the-art MPI broadcast algorithms, demonstrating significant multifold performance gains, especially for large-scale HPC systems. In this paper, we apply this approach to optimization of the MPI Reduce and Allreduce operations. Theoretical analysis and experimental results on a cluster of Grid’5000 platform are presented.