Triple-loop networks with arbitrarily many minimum distance diagrams
Combinatorics
2009-07-07 v1 Discrete Mathematics
Optimization and Control
Abstract
Minimum distance diagrams are a way to encode the diameter and routing information of multi-loop networks. For the widely studied case of double-loop networks, it is known that each network has at most two such diagrams and that they have a very definite form "L-shape''. In contrast, in this paper we show that there are triple-loop networks with an arbitrarily big number of associated minimum distance diagrams. For doing this, we build-up on the relations between minimum distance diagrams and monomial ideals.
Cite
@article{arxiv.0705.3631,
title = {Triple-loop networks with arbitrarily many minimum distance diagrams},
author = {Pilar Sabariego and Francisco Santos},
journal= {arXiv preprint arXiv:0705.3631},
year = {2009}
}