A Branch and Cut Algorithm for the Halfspace Depth Problem
| dc.creator | Chen, Dan | |
| dc.date | 2007-05-14 | |
| dc.date.accessioned | 2026-07-07T08:01:26Z | |
| dc.date.available | 2026-07-07T08:01:26Z | |
| dc.description | The concept of data depth in non-parametric multivariate descriptive statistics is the generalization of the univariate rank method to multivariate data. Halfspace depth is a measure of data depth. Given a set S of points and a point p, the halfspace depth (or rank) k of p is defined as the minimum number of points of S contained in any closed halfspace with p on its boundary. Computing halfspace depth is NP-hard, and it is equivalent to the Maximum Feasible Subsystem problem. In this thesis a mixed integer program is formulated with the big-M method for the halfspace depth problem. We suggest a branch and cut algorithm. In this algorithm, Chinneck's heuristic algorithm is used to find an upper bound and a related technique based on sensitivity analysis is used for branching. Irreducible Infeasible Subsystem (IIS) hitting set cuts are applied. We also suggest a binary search algorithm which may be more stable numerically. The algorithms are implemented with the BCP framework from the COIN-OR project. | |
| dc.description | 110 pages, 25 figures | |
| dc.identifier | https://arxiv.org/abs/0705.1956 | |
| dc.identifier | http://arxiv.org/abs/0705.1956 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/128912 | |
| dc.subject | Computational Geometry | |
| dc.title | A Branch and Cut Algorithm for the Halfspace Depth Problem | |
| dc.type | text |