cs 17(9): e3

Research Article

Necessary & Sufficient Conditions for Consistency of Haar Wavelet Expressions to their resizable Hadoop Cluster Channels and Complexity

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  • @ARTICLE{10.4108/eai.28-6-2017.153490,
        author={Ravinder Prakash G.},
        title={Necessary \& Sufficient Conditions for Consistency of Haar Wavelet Expressions to their resizable Hadoop Cluster Channels and Complexity},
        journal={EAI Endorsed Transactions on Cloud Systems},
        volume={3},
        number={9},
        publisher={EAI},
        journal_a={CS},
        year={2017},
        month={12},
        keywords={Haar Wavelet, Bounded-Capacity, Resizable Hadoop, Cluster Complexity, Discrepancy, Trace Distance Norm, and Finite string Representation},
        doi={10.4108/eai.28-6-2017.153490}
    }
    
  • Ravinder Prakash G.
    Year: 2017
    Necessary & Sufficient Conditions for Consistency of Haar Wavelet Expressions to their resizable Hadoop Cluster Channels and Complexity
    CS
    EAI
    DOI: 10.4108/eai.28-6-2017.153490
Ravinder Prakash G.1,*
  • 1: Senior Professor Research, BMS Institute of Technology & Management Dodaballapur Road, Avalahalli Yelahanka, Bengaluru – 560 064
*Contact email: prakashgravi@gmail.com

Abstract

Abstractβ€”We develop a novel technique for resizable Hadoop cluster’s lower bounds, the bipartite matching rectangular array of Haar Wavelet expressions. Specifically, fix an arbitrary hybrid kernel function 𝒇 ∢ {𝟎, 𝟏}𝒏 β†’ {𝟎, 𝟏} and let 𝑨𝒇 be the rectangular array of Haar Wavelet expressions whose columns are each an application of 𝒇 to some subset of the variables π’™πŸ, π’™πŸ, … , π’™πŸ’π’ . We prove that 𝑨𝒇 has bounded-capacity resizable Hadoop cluster’s complexity 𝛀(𝒅), where 𝒅 is the approximate degree of 𝒇. This finding remains valid in the MapReduce programming model, regardless of prior measurement. In particular, it gives a new and simple proof of lower bounds for robustness and other symmetric conjunctive predicates. We further characterize the discrepancy, approximate PageRank, and approximate trace distance norm of 𝑨𝒇 in terms of well-studied analytic properties of 𝒇, broadly generalizing several findings on small-bias resizable Hadoop cluster and agnostic inference. The method of this paper has also enabled important progress in multi-cloud resizable Hadoop cluster’s complexity.