An extremal problem on trees and database theory

Abstract

We consider an extremal problem on labelled directed trees and applications to database theory. Among others, we will show explicit keysystems on an underlying set of size $n$, that cannot be represented by a database of less than $2^{n(1-c\cdot \log \log n / \log n)}$ rows.

Keywords

• relational database
• minimum matrix representation
• extremal problems
• labelled directed tree
• [info.info-dm] computer science [cs]/discrete mathematics [cs.dm]
• [math.math-co] mathematics [math]/combinatorics [math.co]