Optimal Fraction Repetition Codes for Access-Balancing in Distributed Storage

To solve the access-balancing problem in distributed storage systems, we introduce a new combinatorial model, called MinVar model for fractional repetition (FR) codes. Since FR codes are based on graphs or set our is characterized by property that variance among sums of block-labels incident to fixed vertex minimized. This characterization different from Dau and Milenkovic's MaxMinSum while minimum sum labels maximized. We show meaningful distinguishing labelings with variances but same MaxMin value some By reformulating an equivalent vertex-labeling graphs, find several families optimal balanced access frequency, provide fundamental results both problems. It interesting closely related concept magic-labeling graph theory.