Abstract
A triple system is a collection of b blocks, each of size three, on a set of v points. It is j-balanced when every two j-sets of points appear in numbers of blocks that are as nearly equal as possible, and well balanced when it is j-balanced for each {1,2,3}. Well-balanced systems arise in the minimization of variance in file availability in distributed file systems. It is shown that when a triple system that is 2-balanced and 3-balanced exists, so does one that is well balanced. Using known and new results on variants of group divisible designs, constructions for well-balanced triple systems are developed. Using these, the spectrum of pairs (v,b) for which such a well-balanced triple system exists is determined completely.
Original language | English (US) |
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Pages (from-to) | 77-100 |
Number of pages | 24 |
Journal | Journal of Combinatorial Designs |
Volume | 24 |
Issue number | 2 |
DOIs | |
State | Published - Feb 1 2016 |
Keywords
- candelabra system
- large set
- triple system
- well-balanced design
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics