Asymmetric Key-Value Split Pattern Assumption over MapReduce Behavioral Model

Abstract

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. Keywordsapper, reducer, key-value, asymmetric, split pattern, utilities, MapReduce, behavioral, actual quantifiability