Ensuring that most of data accesses are satisfied from on-chip memories is a critical problem for chip multiprocessors, as the cost of an off-chip access can be very high. Particularly, multiple cores that need to access the off-chip memory system may contend with each other for the same buses/pins to get there. While it is possible to structure on-chip memory space as shared memory or private memory, each of these has its own drawbacks. In an attempt to achieve lower power consumption than these conventional memory architectures, this paper proposes and evaluates an application-specific hybrid memory architecture that has both shared and private components. The approach is built upon the idea of capturing the amount of privately-accessed and shared data across processors through a polyhedral tool, and using this information to guide memory space partitioning across two dimensions, namely, across parallel processors and across shared and private memory components. We evaluate the resulting memory configurations using a set of benchmarks and compare them to pure private and pure shared architectures. When running the same set of applications with the same code optimizations, our results indicate that the proposed hybrid memory design methodology leads to much less power consumption than the conventional architectures.