Computing Multi-Homogeneous Bezout Numbers is Hard
| dc.creator | Malajovich, Gregorio | |
| dc.creator | Meer, Klaus | |
| dc.date | 2004-05-05 | |
| dc.date.accessioned | 2026-07-07T08:38:10Z | |
| dc.date.available | 2026-07-07T08:38:10Z | |
| dc.description | The multi-homogeneous Bezout number is a bound for the number of solutions of a system of multi-homogeneous polynomial equations, in a suitable product of projective spaces. Given an arbitrary, not necessarily multi-homogeneous system, one can ask for the optimal multi-homogenization that would minimize the Bezout number. In this paper, it is proved that the problem of computing, or even estimating the optimal multi-homogeneous Bezout number is actually NP-hard. In terms of approximation theory for combinatorial optimization, the problem of computing the best multi-homogeneous structure does not belong to APX, unless P = NP. Moreover, polynomial time algorithms for estimating the minimal multi-homogeneous Bezout number up to a fixed factor cannot exist even in a randomized setting, unless BPP contains NP. | |
| dc.identifier | https://arxiv.org/abs/cs/0405021 | |
| dc.identifier | http://arxiv.org/abs/cs/0405021 | |
| dc.identifier | Theory of Computing Systems, Volume 40, Number 4 / June, 2007 | |
| dc.identifier | doi:10.1007/s00224-006-1322-y | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/140631 | |
| dc.subject | Computational Complexity | |
| dc.subject | Symbolic Computation | |
| dc.subject | F.2.1;G.1.5 | |
| dc.title | Computing Multi-Homogeneous Bezout Numbers is Hard | |
| dc.type | text |