Irredundant intervals
Combinatorics
2008-02-03 v1
Abstract
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 of intervals on a linearly ordered set of elements, we can construct in 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}.
Keywords
Cite
@article{arxiv.math/9606232,
title = {Irredundant intervals},
author = {Donald E. Knuth},
journal= {arXiv preprint arXiv:math/9606232},
year = {2008}
}