In this paper, we investigate the core-switch mapping(CSM) problem that optimally maps cores onto an NoC architecture such that either the energy consumption or the congestion is minimized. We propose a many-to-many core-switch mapping(mCSM) that allows a switch(core) to have multiple connections to its adjacent cores(switches). We also present decomposition methods that can obtain the suboptimal solutions with enhanced computational efficiency. Our work is the first to provide an exact mixed-integer linear programming(MILP) formulation for the complete CSM problems, including the optimal choice of core placements, switches for each core, and network interfaces for communication flows. Experiments with four random benchmarks show that 4:4 mCSM achieves 81.2% of energy savings and 2.5% of bandwidth savings compared with one-to-one mapping. They also show that, for one-to-one mapping, our optimal solutions obtained by the full MILP save 34.8% of energy consumption and 34.4% of bandwidth requirement compared with those from the existing algorithms.