  This expository note presents simplifications of a theorem due to Gy\H{o}ri
and an algorithm due to Franzblau and Kleitman: Given a family $F$ of $m$
intervals on a linearly ordered set of $n$ elements, we can construct in
$O(m+n)^2$ steps an irredundant subfamily having maximum cardinality, as well
as a generating family having minimum cardinality. The algorithm is of special
interest because it solves a problem analogous to finding a maximum independent
set, but on a class of objects that is more general than a matroid. This note
is also a complete, runnable computer program, which can be used for
experiments in conjunction with the public-domain software of {\sl The Stanford
GraphBase}.
