English

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}
}
R2 v1 2026-06-21T08:31:42.594Z