Weighted cache location problem with identical servers.(English)Zbl 1442.68011

Summary: This paper extends the well-known $$p$$-CLP with one server to $$p$$-CLP with $$m \geq 2$$ 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.

MSC:

 68M10 Network design and communication in computer systems 68M12 Network protocols 68R10 Graph theory (including graph drawing) in computer science 68W10 Parallel algorithms in computer science 68W40 Analysis of algorithms 90C35 Programming involving graphs or networks
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