Weighted Cache Location Problem with Identical Servers

• Published in: Journal of Applied Mathematics Vol. 2014; no. 2014; pp. 421 - 431-545
• Main Authors: Wang, Hongfa, Ding, Wei
• Format: Journal Article
• Language: English
• Published: Cairo, Egypt Hindawi Limiteds 01.01.2014; Hindawi Publishing Corporation; John Wiley & Sons, Inc; Wiley
• Subjects: Algorithms; Dynamic programming; Equivalence; Heuristic; Networks; Production scheduling; Running; Series (mathematics); Servers; Servers (computers); Trees
• ISSN: 1110-757X; 1687-0042; 1687-0042
• DOI: 10.1155/2014/586146

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 ( p h 2 + n ) -time parallel exact algorithm for p -CLP on a tree and then present a parallel exact algorithm with at most O ( ( 4 / 9 ) p 2 n 2 ) 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.