Border basis detection is NP-complete

Details Border basis detection is NP-complete Border basis detection is NP-complete

2010-11-28

arxiv.org/abs/1011.6021v1

Computer Science

Computational Complexity

18 pages

Scientific paper

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.

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