Suppose we want to replicate a file over a collection of n servers, labeled s1, s2,…, Sn. To place a copy of the file at server St results in a placement cost of ci, for an integerci > 0.
Now, if a user requests the file from server Si, and no copy of the file is present at Si, then the servers Si+1, Si+2, Si+3 … are searched in order until a copy of the file is finally found, say at server Sj, where j > i. This results in an access cost of j – i. (Note that the lower-indexed servers S–1, Si—2,... are not consulted in this search.) The access cost is 0 if Si holds a copy of the file. We will require that a copy of the file be placed at server Sn, so that all such searches will terminate, at the latest, at Sn.
We'd like to place copies of the files at the servers so as to minimize the sum of placement and access costs. Formally, we say that a configuration is a choice, for each server St with i = 1, 2, n – 1, of whether to place a copy of the file at St or not. (Recall that a copy is always placed at Sn.) The total cost of a configuration is the sum of all placement costs for servers with a copy of the file, plus the sum of all access costs associated with all n servers.
Give a polynomial-time algorithm to find a configuration of minimum total cost.
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