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The paper is regarding the fair distribution of several files having different sizes to several storage supports. With the existence of several storage supports and different files, we search for a method that makes an appropriate backup. The appropriate backup guarantees a fair distribution of the big data (files). Fairness is related to the used spaces of storage support distribution. The problem is how to find a fair method that stores all files on the available storage supports, where each file is characterized by its size. We propose in this paper some fairness methods that seek to minimize the gap between used spaces of all storage supports. In this paper, several algorithms are developed to solve the proposed problem, and the experimental study shows the performance of these developed algorithms. [ABSTRACT FROM AUTHOR]