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 \({3 \over 2}\)-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.
T. Ito—Supported by JST CREST Grant Number JPMJCR1402, Japan, and JSPS KAKENHI Grant Number JP16K00004.
N. Kakimura—Supported by JST ERATO Grant Number JPMJER1201, Japan, and by JSPS KAKENHI Grant Number JP17K00028.
N. Kamiyama—Supported by JST PRESTO Grant Number JPMJPR14E1, Japan.
Y. Kobayashi—Supported by JST ERATO Grant Number JPMJER1201, Japan, and by JSPS KAKENHI Grant Numbers JP16K16010 and JP16H03118.
Y. Okamoto—Supported by Kayamori Foundation of Informational Science Advancement, JST CREST Grant Number JPMJCR1402, Japan, and JSPS KAKENHI Grant Numbers JP24106005, JP24700008, JP24220003, JP15K00009.
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Notes
- 1.
The reader may wonder why the authors did not make a semi-log plot, which could show the trend better. However, this was impossible since some instances were solved in “0 ms,” and taking the logarithm produced \(-\infty \).
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We thank Eiji Oki for bringing the problem into our attention.
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Ito, T., Kakimura, N., Kamiyama, N., Kobayashi, Y., Okamoto, Y., Shiitada, T. (2018). Tight Approximability of the Server Allocation Problem for Real-Time Applications. In: Alistarh, D., Delis, A., Pallis, G. (eds) Algorithmic Aspects of Cloud Computing. ALGOCLOUD 2017. Lecture Notes in Computer Science(), vol 10739. Springer, Cham. https://doi.org/10.1007/978-3-319-74875-7_4
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