English

Border basis detection is NP-complete

Computational Complexity 2010-11-30 v1

Abstract

Border basis detection (BBD) is described as follows: given a set of generators of an ideal, decide whether that set of generators is a border basis of the ideal with respect to some order ideal. The motivation for this problem comes from a similar problem related to Gr\"obner bases termed as Gr\"obner basis detection (GBD) which was proposed by Gritzmann and Sturmfels (1993). GBD was shown to be NP-hard by Sturmfels and Wiegelmann (1996). In this paper, we investigate the computational complexity of BBD and show that it is NP-complete.

Cite

@article{arxiv.1011.6021,
  title  = {Border basis detection is NP-complete},
  author = {Prabhanjan V. Ananth and Ambedkar Dukkipati},
  journal= {arXiv preprint arXiv:1011.6021},
  year   = {2010}
}

Comments

18 pages

R2 v1 2026-06-21T16:49:52.825Z