Asymmetric Key-Value Split Pattern Assumption over MapReduce Behavioral Model

Actual Quantifiability is a concept in MapReduce that is based on two assumptions: (1) every mapper is cautious, i. e. , does not exclude any reducer's key-value split pattern choice from consideration, and (2) every mapper respects the reducer's key-value split pattern preferences, i. e. , deems one reducer's key-value split pattern choice to be infinitely more likely than another whenever it premises the reducer to prefer the one to the other. In this paper we provide a new approach for actual quantifiability, by assuming that mappers have asymmetric key-value split pattern about the reducer's key-value utilities. We show that, if the uncertainty of each mapper about the reducer's key-value utilities vanishes gradually in some regular manner, then the key-value split pattern choices it can quantifiably make under common conjecture in quantifiability are all actually quantifiable in the original MapReduce with no uncertainty about the reducer's utilities.