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Article overview
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Bounds on data limits for all-to-all comparison from combinatorial designs | | Joanne Hall
; Daniel Horsley
; Douglas R. Stinson
; | | Date: |
1 Sep 2023 | | Abstract: | In situations where every item in a data set must be compared with every
other item in the set, it may be desirable to store the data across a number of
machines in such a way that any two data items are stored together on at least
one machine. One way to evaluate the efficiency of such a distribution is by
the largest fraction of the data it requires to be allocated to any one
machine. The all-to-all comparison (ATAC) data limit for $m$ machines is a
measure of the minimum of this value across all possible such distributions. In
this paper we further the study of ATAC data limits. We observe relationships
between them and the previously studied combinatorial parameters of fractional
matching numbers and covering numbers. We also prove a lower bound on the ATAC
data limit that improves on one of Hall, Kelly and Tian, and examine the
special cases where equality in this bound is possible. Finally, we investigate
the data limits achievable using various classes of combinatorial designs. In
particular, we examine the cases of transversal designs and projective
Hjelmslev planes. | | Source: | arXiv, 2309.00213 | | Services: | Forum | Review | PDF | Favorites | |
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