Basis enumeration of hyperplane arrangements up to symmetries
| dc.contributor.advisor | Bremner, David | |
| dc.contributor.author | Moss, Aaron | |
| dc.date.accessioned | 2023-03-01T16:43:55Z | |
| dc.date.available | 2023-03-01T16:43:55Z | |
| dc.date.issued | 2012 | |
| dc.date.updated | 2023-03-01T15:03:12Z | |
| dc.description.abstract | This thesis details a method of enumerating bases of hyperplane arrangements up to symmetries. I consider here automorphisms, geometric symmetries which leave the set of all points contained in the arrangement setwise invariant. The algorithm for basis enumeration described in this thesis is a backtracking search over the adjacency graph implied on the bases by minimum-ratio simplex pivots, pruning at bases symmetric to those already seen. This work extends Bremner, Sikiric, and Schiirmann's method for basis enumeration of polyhedra up to symmetries, including a new pivoting rule for finding adjacent bases in arrangements, a method of computing automorphisms of arrangements which extends the method of Bremner et al. for computing automorphisms of polyhedra, and some associated changes to optimizations used in the previous work. I include results of tests on ACEnet clusters showing an order of magnitude speedup from the use of C++ in my implementation, an up to 3x speedup with a 6-core parallel variant of the algorithm, and positive results from other optimizations. | |
| dc.description.copyright | © Aaron Moss, 2012 | |
| dc.format | text/xml | |
| dc.format.extent | viii, 69 pages | |
| dc.format.medium | electronic | |
| dc.identifier.oclc | (OCoLC)1342601301 | en |
| dc.identifier.other | Thesis 9102 | en |
| dc.identifier.uri | https://unbscholar.lib.unb.ca/handle/1882/14398 | |
| dc.language.iso | en_CA | |
| dc.publisher | University of New Brunswick | |
| dc.rights | http://purl.org/coar/access_right/c_abf2 | |
| dc.subject.discipline | Computer Science | |
| dc.subject.lcsh | Hyperspace. | en |
| dc.subject.lcsh | Symmetry. | en |
| dc.subject.lcsh | Algorithms. | en |
| dc.subject.lcsh | Polyhedra. | en |
| dc.title | Basis enumeration of hyperplane arrangements up to symmetries | |
| dc.type | master thesis | |
| thesis.degree.discipline | Computer Science | |
| thesis.degree.fullname | Master of Computer Science | |
| thesis.degree.grantor | University of New Brunswick | |
| thesis.degree.level | masters | |
| thesis.degree.name | M.C.S. |
Files
Original bundle
1 - 1 of 1