Reconfigurable computers (RCs) host multiple field programmable gate arrays (FPGAs) and one or more physical memories that communicate through an interconnection fabric. State-of-the-art RCs provide abundant hardware and storage resources, but have tight constraints on FPGA pin-out and inter-FPGA interconnection resources. These stringent constraints are the primary impediment for multi-FPGA partitioning tools to generate high-quality designs, in this paper, we present two integrated partitioning and synthesis approaches for RCs. The first approach involves fine-grained partitioning of a scheduled data-flow graph (DFG, or an operation graph), and the second involves a coarse-grained partitioning of an unscheduled control data flow graph (CDFG, or a block graph). A hardware design space exploration engine is integrated with the block graph partitioner that dynamically contemplates multiple schedules during partitioning. The novel feature in the partitioning approaches is that the physical memory in the RC is effectively used to alleviate the FPGA pin-out and inter-FPGA interconnection bottle-neck. Several experiments have been conducted, targeting commercial multi-FPGA boards, to compare the two partitioning approaches, and detailed summaries are presented.