Infeasibility of Systems of Halfspaces (2001)
BibTeX
@MISC{Felsner01infeasibilityof,
author = {Stefan Felsner and Nicole Morawe},
title = {Infeasibility of Systems of Halfspaces},
year = {2001}
}
Bookmark
 |
 |
 |
 |
 |
 |
OpenURL
Abstract
An oriented hyperplane is a hyperplane with designated good and bad sides. The infeasibility of a cell in an arrangement ~ A of oriented hyperplanes is the number of hyperplanes with this cell on the bad side. Wit MinInf( ~ A) we denote the minimum infeasibility of a cell in the arrangement. A subset of hyperplanes of ~ A is called an infeasible subsystem if every cell in the induced subarrangement has positive infeasibility. With MaxDis( ~ A) we denote the maximal number of disjoint infeasible subsystems of ~ A. For every arrangement ~ A of oriented hyperplanes MinInf( ~ A) MaxDis( ~ A): In this paper we investigate bounds for the ratio of the LHS over the RHS in the above inequality. The main contribution is a detailed discussion of the problem in the case d = 2, i.e., for 2-dimensional arrangements. We prove that MinInf( ~ A) 2 MaxDis( ~ A), in this case. An example shows that the factor 2 is best possible. If an arrangement ~ A of n lines contains a ...
Citations
| 29 | Arrangements of hyperplanes, higher braid groups and higher Bruhat orders - Manin - 1989 |
| 27 | A minimax theorem for directed graphs - Lucchesi, Younger - 1978 |
| 23 | Higher Bruhat Orders and Cyclic Hyperplane Arrangements, Topology 32 - Ziegler - 1993 |
| 13 | How to make a digraph strongly connected - Frank - 1981 |
| 10 | Zonotopes associated with higher Bruhat orders - FELSNER, ZIEGLER |
| 10 | Pseudoline arrangements - Goodman - 1997 |
| 7 | Sweeps, arrangements and signotopes - Felsner, Weil - 2001 |
| 4 | Triangles in Euclidean arrangements - Felsner, Kriegel - 1999 |
| 3 | A theorem on higher Bruhat orders - Felsner, Weil |
| 2 | Sweeps, arrangements and signotopes, Discrete Appl.Math - Felsner, Weil |
| 2 | Teilungen der Ebenen durch Geraden oder topologische - Ringel - 1956 |
| 1 | asz, On two minimax theorems in graph - Lov - 1976 |
