### Abstract

The server allocation problem is a facility location problem for a distributed processing scheme on a real-time network. In this problem, we are given a set of users and a set of servers. Then, we consider the following communication process between users and servers. First a user sends his/her request to the nearest server. After receiving all the requests from users, the servers share the requests. A user will then receive the data processed from the nearest server. The goal of this problem is to choose a subset of servers so that the total delay of the above process is minimized. In this paper, we prove the following approximability and inapproximability results. We first show that the server allocation problem has no polynomial-time approximation algorithm unless P = NP. However, assuming that the delays satisfy the triangle inequality, we design a polynomial-time 3/2-approximation algorithm. When we assume the triangle inequality only among servers, we propose a polynomial-time 2-approximation algorithm. Both of the algorithms are tight in the sense that we cannot obtain better polynomial-time approximation algorithms unless P = NP. Furthermore, we evaluate the practical performance of our algorithms through computational experiments, and show that our algorithms scale better and produce comparable solutions than the previously proposed method based on integer linear programming.

Original language | English |
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Title of host publication | Algorithmic Aspects of Cloud Computing - 3rd International Workshop, ALGOCLOUD 2017, Revised Selected Papers |

Publisher | Springer Verlag |

Pages | 41-55 |

Number of pages | 15 |

ISBN (Print) | 9783319748740 |

DOIs | |

Publication status | Published - 2018 Jan 1 |

Event | 3rd International Workshop on Algorithmic Aspects of Cloud Computing, ALGOCLOUD 2017 - Vienna, Austria Duration: 2017 Sep 5 → 2017 Sep 5 |

### 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 | 10739 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 3rd International Workshop on Algorithmic Aspects of Cloud Computing, ALGOCLOUD 2017 |
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Country | Austria |

City | Vienna |

Period | 17/9/5 → 17/9/5 |

### Fingerprint

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Algorithmic Aspects of Cloud Computing - 3rd International Workshop, ALGOCLOUD 2017, Revised Selected Papers*(pp. 41-55). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10739 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-319-74875-7_4

**Tight approximability of the server allocation problem for real-time applications.** / Ito, Takehiro; Kakimura, Naonori; Kamiyama, Naoyuki; Kobayashi, Yusuke; Okamoto, Yoshio; Shiitada, Taichi.

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

*Algorithmic Aspects of Cloud Computing - 3rd International Workshop, ALGOCLOUD 2017, Revised Selected Papers.*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 10739 LNCS, Springer Verlag, pp. 41-55, 3rd International Workshop on Algorithmic Aspects of Cloud Computing, ALGOCLOUD 2017, Vienna, Austria, 17/9/5. https://doi.org/10.1007/978-3-319-74875-7_4

}

TY - GEN

T1 - Tight approximability of the server allocation problem for real-time applications

AU - Ito, Takehiro

AU - Kakimura, Naonori

AU - Kamiyama, Naoyuki

AU - Kobayashi, Yusuke

AU - Okamoto, Yoshio

AU - Shiitada, Taichi

PY - 2018/1/1

Y1 - 2018/1/1

N2 - The server allocation problem is a facility location problem for a distributed processing scheme on a real-time network. In this problem, we are given a set of users and a set of servers. Then, we consider the following communication process between users and servers. First a user sends his/her request to the nearest server. After receiving all the requests from users, the servers share the requests. A user will then receive the data processed from the nearest server. The goal of this problem is to choose a subset of servers so that the total delay of the above process is minimized. In this paper, we prove the following approximability and inapproximability results. We first show that the server allocation problem has no polynomial-time approximation algorithm unless P = NP. However, assuming that the delays satisfy the triangle inequality, we design a polynomial-time 3/2-approximation algorithm. When we assume the triangle inequality only among servers, we propose a polynomial-time 2-approximation algorithm. Both of the algorithms are tight in the sense that we cannot obtain better polynomial-time approximation algorithms unless P = NP. Furthermore, we evaluate the practical performance of our algorithms through computational experiments, and show that our algorithms scale better and produce comparable solutions than the previously proposed method based on integer linear programming.

AB - The server allocation problem is a facility location problem for a distributed processing scheme on a real-time network. In this problem, we are given a set of users and a set of servers. Then, we consider the following communication process between users and servers. First a user sends his/her request to the nearest server. After receiving all the requests from users, the servers share the requests. A user will then receive the data processed from the nearest server. The goal of this problem is to choose a subset of servers so that the total delay of the above process is minimized. In this paper, we prove the following approximability and inapproximability results. We first show that the server allocation problem has no polynomial-time approximation algorithm unless P = NP. However, assuming that the delays satisfy the triangle inequality, we design a polynomial-time 3/2-approximation algorithm. When we assume the triangle inequality only among servers, we propose a polynomial-time 2-approximation algorithm. Both of the algorithms are tight in the sense that we cannot obtain better polynomial-time approximation algorithms unless P = NP. Furthermore, we evaluate the practical performance of our algorithms through computational experiments, and show that our algorithms scale better and produce comparable solutions than the previously proposed method based on integer linear programming.

UR - http://www.scopus.com/inward/record.url?scp=85042553791&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85042553791&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-74875-7_4

DO - 10.1007/978-3-319-74875-7_4

M3 - Conference contribution

AN - SCOPUS:85042553791

SN - 9783319748740

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

SP - 41

EP - 55

BT - Algorithmic Aspects of Cloud Computing - 3rd International Workshop, ALGOCLOUD 2017, Revised Selected Papers

PB - Springer Verlag

ER -