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Access balancing in storage systems by labeling partial Steiner systems

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Abstract

Storage architectures ranging from minimum bandwidth regenerating encoded distributed storage systems to declustered-parity RAIDs can employ dense partial Steiner systems to support fast reads, writes, and recovery of failed storage units. To enhance performance, popularities of the data items should be taken into account to make frequencies of accesses to storage units as uniform as possible. A combinatorial model ranks items by popularity and assigns data items to elements in a dense partial Steiner system so that the sums of ranks of the elements in each block are as equal as possible. By developing necessary conditions in terms of independent sets, we demonstrate that certain Steiner systems must have a much larger difference between the largest and smallest block sums than is dictated by an elementary lower bound. In contrast, we also show that certain dense partial \(S(t,t+1,v)\) designs can be labeled to realize the elementary lower bound. Furthermore, we prove that for every admissible order v, there is a Steiner triple system (S(2, 3, v)) whose largest difference in block sums is within an additive constant of the lower bound.

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Authors and Affiliations

  1. Industrial Systems Engineering and Management, National University of Singapore, Singapore, Singapore

    Yeow Meng Chee

  2. Computing, Informatics, and Decision Systems Engineering, Arizona State University, Tempe, AZ, USA

    Charles J. Colbourn & Dylan Lusi

  3. Computer Science and Information Technology, RMIT University, Melbourne, Australia

    Hoang Dau

  4. Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, Urbana, IL, USA

    Ryan Gabrys & Olgica Milenkovic

  5. Computer Science, University of Vermont, Burlington, VT, USA

    Alan C. H. Ling

Authors
  1. Yeow Meng Chee
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  2. Charles J. Colbourn
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  3. Hoang Dau
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  4. Ryan Gabrys
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  5. Alan C. H. Ling
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  6. Dylan Lusi
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  7. Olgica Milenkovic
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Correspondence to Charles J. Colbourn.

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Communicated by M. Buratti.

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The work was supported by NSF Grants CCF 1816913 (CJC) and 1814298 (OM).

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Chee, Y.M., Colbourn, C.J., Dau, H. et al. Access balancing in storage systems by labeling partial Steiner systems. Des. Codes Cryptogr. 88, 2361–2376 (2020). https://doi.org/10.1007/s10623-020-00786-z

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  • DOI: https://doi.org/10.1007/s10623-020-00786-z

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