The document discusses two primary data exchange methods in parallel platforms: shared-address-space machines and message-passing platforms. Shared-address-space platforms allow multiple processors to access a common memory, distinguished by uniform (UMA) and non-uniform memory access (NUMA) architectures, each impacting algorithm design and programming complexity. Message-passing platforms, on the other hand, consist of independent processors with their own exclusive memory, and while requiring less hardware support, they are more challenging to emulate in a shared-address-space environment.