Weighted Cache Location Problem with Identical Servers

This paper extends the well-known p-CLP with one server to p-CLP with m≥2 identical servers, denoted by (p,m)-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 (p,m)-CLP under CSOP to (p,m)-CSOP CLP and investigate that (p,m)-CSOP CLP on a general network is equivalent to that on a forest and further to multiple CLPs on trees. The case of m=2 is the focus of this paper. We first devise an improved O(ph2+n)-time parallel exact algorithm for p-CLP on a tree and then present a parallel exact algorithm with at most O((4/9)p2n2) time in the worst case for (p,2)-CSOP CLP on a general network. Furthermore, we extend the idea of parallel algorithm to the cases of m>2 to obtain a worst-case O((4/9)(n-m)2((m+p)p/p-1!))-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