Closed-form mapping conditions for the synthesis of linear processor arrays

This paper addresses the problem of mapping algorithms with constant data dependences to linear processor arrays. The closed-form necessary and suucient mapping conditions are derived to identify mappings without computational connicts and data link collisions. These mapping conditions depend on the space-time mapping matrix and the problem size parameters only. Their correctness can be veriied in constant time that is independent of problem size. The design of optimal linear processor arrays is formulated as a mathematic programming problem, which can be solved eeciently by a systematic enumeration of a polynomial search space.