[SOLVED] algorithm 1.

1.
Textbook Exercise 15.3.2

2.
Textbook Exercise 15.4.1

3.
Textbook Exercise 24.1-1

4.
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 serverresults in a placement cost of , for an integer> 0. Now, if a user requests the file from server , and no copy of the file is present at , 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 , , are not consulted in this search.) The access cost is 0 ifholds 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.

Wed 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 serverwith i = 1,2,,n-1, of whether to place a copy of the file ator 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 the minimum total cost. What is the running time of your algorithm?