English

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 FF of mm intervals on a linearly ordered set of nn elements, we can construct in O(m+n)2O(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}.

Keywords

Cite

@article{arxiv.math/9606232,
  title  = {Irredundant intervals},
  author = {Donald E. Knuth},
  journal= {arXiv preprint arXiv:math/9606232},
  year   = {2008}
}