# Online Algorithms for Leasing Vertex Cover and Leasing Non-metric Facility Location

### Christine Markarian, Friedhelm der Heide

#### Abstract

We consider leasing variants of two classical N P-hard optimization problems, Vertex Cover (VC) and non-metric Facility Location (non-metric FL). These contain the well-known Parking Permit problem due to Meyerson [FOCS 2005] as a special sub-case and can be found as sub-problems in many operations research applications. We give the first online algorithms for these two problems, evaluated using the standard notion of competitive analysis in which the online algorithm whose input instance is revealed over time is compared to the optimal offline algorithm which knows the entire input sequence in advance and is optimal. Our algorithms have optimal and near-optimal competitive ratios for the leasing variants of VC and non-metric FL, respectively.

Download#### Paper Citation

#### in Harvard Style

Markarian C. and der Heide F. (2019). **Online Algorithms for Leasing Vertex Cover and Leasing Non-metric Facility Location**.In *Proceedings of the 8th International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,* ISBN 978-989-758-352-0, pages 315-321. DOI: 10.5220/0007369503150321

#### in Bibtex Style

@conference{icores19,

author={Christine Markarian and Friedhelm der Heide},

title={Online Algorithms for Leasing Vertex Cover and Leasing Non-metric Facility Location},

booktitle={Proceedings of the 8th International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,},

year={2019},

pages={315-321},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0007369503150321},

isbn={978-989-758-352-0},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 8th International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,

TI - Online Algorithms for Leasing Vertex Cover and Leasing Non-metric Facility Location

SN - 978-989-758-352-0

AU - Markarian C.

AU - der Heide F.

PY - 2019

SP - 315

EP - 321

DO - 10.5220/0007369503150321