.+Suppose+there+is+an+optimal+solution+where+files+are+not+sorted+in+the+increasing+order+of+li/pi.+Then%2C+there+must+be+a+neighboring+pair+(a%2Cb)%2C+such+that+la/pa+%3E+lb/pb+and+yet+a+is+stored+before+b.+We+show+that+interchaging+their+order+reduces+the+expected+retrieval+cost.+Since+a%2C+b+are+neighbors%2C+interchanging+their+order+does+not+affect+the+retrieval+cost+for+any+other+files.+Thus%2C+the+only+change+in+the+summation+defining+T+is+for+the+terms+corresponding+to+a+and+b.+The+retrieval+cost+before+the+swap+is:+pa(L%2Bla)%2Bpb(L%2Bla%2Blb)+where+L+is+the+total+length+of+files+preceding+a.+After+the+swap%2C+the+cost+for+accessing+a+and+b+is:+pb(L%2Blb)%2Bpa(L%2Bla%2Blb).+Suppose+the+swap+did+not+reduce+the+cost.+Then%2C.jpg)
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