# Algorithmic View of Online Prize-collecting Optimization Problems

### Christine Markarian, Abdul El-Kassar

#### Abstract

Online algorithms have been a cornerstone of research in network design problems. Unlike in classical offline algorithms, the input to an online algorithm is revealed in portions over time and the online algorithm reacts to each portion while targeting a given optimization goal. Online algorithms are deployed in real-world optimization problems in which provably good decisions are expected in the present without knowing the future. In this paper, we consider a well-established branch of online optimization problems, known as online prize-collecting problems, in which the online algorithm may reject some input portions at the cost of paying an associated penalty. These appear in business applications in which a company decides to lose some customers by paying an associated penalty. Particularly, we study the online prize-collecting variants of three well-known optimization problems: Connected Dominating Set, Vertex Cover, and Non-metric Facility Location, namely, Online Prize-collecting Connected Dominating Set (OPC-CDS), Online Prize-collecting Vertex Cover (OPC-VC), and Online Prize-collecting Non-metric Facility Location (OPC-NFL), respectively. We propose the first online algorithms for these variants and evaluate them using competitive analysis, the standard framework to measure online algorithms, in which the online algorithm is measured against the optimal offline algorithm that knows the entire input sequence in advance and is optimal.

Download#### Paper Citation

#### in Harvard Style

Markarian C. and El-Kassar A. (2021). **Algorithmic View of Online Prize-collecting Optimization Problems**. In *Proceedings of the 23rd International Conference on Enterprise Information Systems - Volume 1: ICEIS,* ISBN 978-989-758-509-8, pages 744-751. DOI: 10.5220/0010471507440751

#### in Bibtex Style

@conference{iceis21,

author={Christine Markarian and Abdul El-Kassar},

title={Algorithmic View of Online Prize-collecting Optimization Problems},

booktitle={Proceedings of the 23rd International Conference on Enterprise Information Systems - Volume 1: ICEIS,},

year={2021},

pages={744-751},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0010471507440751},

isbn={978-989-758-509-8},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 23rd International Conference on Enterprise Information Systems - Volume 1: ICEIS,

TI - Algorithmic View of Online Prize-collecting Optimization Problems

SN - 978-989-758-509-8

AU - Markarian C.

AU - El-Kassar A.

PY - 2021

SP - 744

EP - 751

DO - 10.5220/0010471507440751