Weighted Cache Location Problem with Identical Servers

Abstract

This paper extends the well-knownp-CLP with one server top-CLP withm≥2identical 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 ofm=2is the focus of this paper. We first devise an improvedO(ph2+n)-time parallel exact algorithm forp-CLP on a tree and then present a parallel exact algorithm with at mostO((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 ofm>2to obtain a worst-caseO((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.