As more processing cores are added to embedded systems processors, the relationships between cores and memories have more influence on the energy consumption of the processor. In this paper, we conduct fundamental research to explore the effects of memory sharing on energy in a multicore processor. We study the Memory Arrangement (MA) Problem. We prove that the general case of MA is NP-complete. We present an optimal algorithm for solving linear MA and optimal and heuristic algorithms for solving rectangular MA. On average, we can produce arrangements that consume 49% less energy than an all shared memory arrangement and 14% less energy than an all private memory arrangement for randomly generated instances. For DSP benchmarks, we can produce arrangements that, on average, consume 20% less energy than an all shared memory arrangement and 27% less energy than an all private memory arrangement.