### Abstract

We consider the online facility assignment problem, with a set of facilities F of equal capacity l in metric space and customers arriving one by one in an online manner. We must assign customer c_{i} to facility f_{j} before the next customer c_{i+1} arrives. The cost of this assignment is the distance between c_{i} and f_{j}. The total number of customers is at most |F|l and each customer must be assigned to a facility. The objective is to minimize the sum of all assignment costs. We first consider the case where facilities are placed on a line so that the distance between adjacent facilities is the same and customers appear anywhere on the line. We describe a greedy algorithm with competitive ratio 4|F| and another one with competitive ratio |F|. Finally, we consider a variant in which the facilities are placed on the vertices of a graph and two algorithms in that setting.

Original language | English (US) |
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Title of host publication | WALCOM |

Subtitle of host publication | Algorithms and Computation - 12th International Conference, WALCOM 2018, Proceedings |

Publisher | Springer-Verlag |

Pages | 156-168 |

Number of pages | 13 |

ISBN (Print) | 9783319751719 |

DOIs | |

State | Published - Jan 1 2018 |

Event | 12th International Conference and Workshop on Algorithms and Computation, WALCOM 2018 - Dhaka, Bangladesh Duration: Mar 3 2018 → Mar 5 2018 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 10755 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 12th International Conference and Workshop on Algorithms and Computation, WALCOM 2018 |
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Country | Bangladesh |

City | Dhaka |

Period | 3/3/18 → 3/5/18 |

### Fingerprint

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*WALCOM: Algorithms and Computation - 12th International Conference, WALCOM 2018, Proceedings*(pp. 156-168). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10755 LNCS). Springer-Verlag. https://doi.org/10.1007/978-3-319-75172-6_14

**Online facility assignment.** / Ahmed, Abu Reyan; Rahman, Md Saidur; Kobourov, Stephen G.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*WALCOM: Algorithms and Computation - 12th International Conference, WALCOM 2018, Proceedings.*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 10755 LNCS, Springer-Verlag, pp. 156-168, 12th International Conference and Workshop on Algorithms and Computation, WALCOM 2018, Dhaka, Bangladesh, 3/3/18. https://doi.org/10.1007/978-3-319-75172-6_14

}

TY - GEN

T1 - Online facility assignment

AU - Ahmed, Abu Reyan

AU - Rahman, Md Saidur

AU - Kobourov, Stephen G

PY - 2018/1/1

Y1 - 2018/1/1

N2 - We consider the online facility assignment problem, with a set of facilities F of equal capacity l in metric space and customers arriving one by one in an online manner. We must assign customer ci to facility fj before the next customer ci+1 arrives. The cost of this assignment is the distance between ci and fj. The total number of customers is at most |F|l and each customer must be assigned to a facility. The objective is to minimize the sum of all assignment costs. We first consider the case where facilities are placed on a line so that the distance between adjacent facilities is the same and customers appear anywhere on the line. We describe a greedy algorithm with competitive ratio 4|F| and another one with competitive ratio |F|. Finally, we consider a variant in which the facilities are placed on the vertices of a graph and two algorithms in that setting.

AB - We consider the online facility assignment problem, with a set of facilities F of equal capacity l in metric space and customers arriving one by one in an online manner. We must assign customer ci to facility fj before the next customer ci+1 arrives. The cost of this assignment is the distance between ci and fj. The total number of customers is at most |F|l and each customer must be assigned to a facility. The objective is to minimize the sum of all assignment costs. We first consider the case where facilities are placed on a line so that the distance between adjacent facilities is the same and customers appear anywhere on the line. We describe a greedy algorithm with competitive ratio 4|F| and another one with competitive ratio |F|. Finally, we consider a variant in which the facilities are placed on the vertices of a graph and two algorithms in that setting.

UR - http://www.scopus.com/inward/record.url?scp=85043319460&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85043319460&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-75172-6_14

DO - 10.1007/978-3-319-75172-6_14

M3 - Conference contribution

SN - 9783319751719

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 156

EP - 168

BT - WALCOM

PB - Springer-Verlag

ER -