# Complexity and Approximability of Hyperplane Covering Problems

### Michael Khachay

#### Abstract

The well known N.Megiddo complexity result for Point Cover Problem on the plane is extended onto $d$-dimensional space (for any fixed $d$). It is proved that Min-$d$PC problem is $L$-reducible to Min-$(d+1)$PC problem, therefore for any fixed $d>1$ there is no PTAS for Min-$d$PC problem, unless $P=NP.$

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#### Paper Citation

#### in Harvard Style

Khachay M. (2013). **Complexity and Approximability of Hyperplane Covering Problems** . In *Proceedings of the 4th International Workshop on Image Mining. Theory and Applications - Volume 1: IMTA-4, (VISIGRAPP 2013)* ISBN 978-989-8565-50-1, pages 109-113. DOI: 10.5220/0004394601090113

#### in Bibtex Style

@conference{imta-413,

author={Michael Khachay},

title={Complexity and Approximability of Hyperplane Covering Problems},

booktitle={Proceedings of the 4th International Workshop on Image Mining. Theory and Applications - Volume 1: IMTA-4, (VISIGRAPP 2013)},

year={2013},

pages={109-113},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0004394601090113},

isbn={978-989-8565-50-1},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 4th International Workshop on Image Mining. Theory and Applications - Volume 1: IMTA-4, (VISIGRAPP 2013)

TI - Complexity and Approximability of Hyperplane Covering Problems

SN - 978-989-8565-50-1

AU - Khachay M.

PY - 2013

SP - 109

EP - 113

DO - 10.5220/0004394601090113