Path independence in serial—parallel data processing

Abstract

For data processing procedures that use splitting data into auxilliary components as a method of problem simplification, their algebraic aspects are discussed. In these procedures, individual components are processed and the results obtained are merged for further processing. Consideration is given to the types of problems where these procedures provide the same result as simultaneous (one-stage) processing of the entire data array. C.R. Plott was the first to introduce this notion of invariance of procedure outcome named ‘path independence’ and study it as applied to choice functions. We generalized this property, extending it to a rather wide scope of problems. The semigroup nature of path independence is demonstrated.