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Journal of Applied Mathematics
Volume 2014, Article ID 586146, 11 pages
http://dx.doi.org/10.1155/2014/586146
Research Article

Weighted Cache Location Problem with Identical Servers

Zhejiang University of Water Resources and Electric Power, Hangzhou, Zhejiang 310018, China

Received 16 February 2014; Revised 20 June 2014; Accepted 4 August 2014; Published 24 August 2014

Academic Editor: Qi Cheng

Copyright © 2014 Hongfa Wang and Wei Ding. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper extends the well-known -CLP with one server to -CLP with identical servers, denoted by -CLP. We propose the closest server orienting protocol (CSOP), under which every client connects to the closest server to itself via a shortest route on given network. We abbreviate -CLP under CSOP to -CSOP CLP and investigate that -CSOP CLP on a general network is equivalent to that on a forest and further to multiple CLPs on trees. The case of is the focus of this paper. We first devise an improved -time parallel exact algorithm for -CLP on a tree and then present a parallel exact algorithm with at most time in the worst case for -CSOP CLP on a general network. Furthermore, we extend the idea of parallel algorithm to the cases of to obtain a worst-case -time exact algorithm. At the end of the paper, we first give an example to illustrate our algorithms and then make a series of numerical experiments to compare the running times of our algorithms.