Blocking sets have one property useful when solving optimization problems.
Suppose we have a finite set $E$ of elements, and real-valued function
$f:E\to R$; we can treat $f(x)$ as the "weight" of element $x\in E$.
Suppose further that we have some family $\A$ of subsets of $E$.
The weight of a member $A\in \A$ is the maximum weight of its element,
that is, $f(A)=\max\{f(x)\colon x\in A\}$. Given a family
$\A$, our goal is to find
the smallest weight of its member. This is a minimization
problem. Using blocking sets we can turn it into a maximization
problems as follows.
Theorem [Edmonds-Fulkerson 1979]: For every antichain $\A$,
\[
\min_{A\in \A}\ \max_{x\in A}f(x)=\max_{B\in b(\A)}\ \min_{x\in B}f(x)\,.
\]
Related literature:
J. Edmonds and D.R. Fulkerson, Bottleneck extrema,
Journal of Combinatorial Theory, 8, 299-306 (1970)
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