Abstract: The system and method disclosed herein are for use in data processing apparatus which is operated as a paging machine and wherein a program is considered a page reference string. The system and method effect the determination of the minimum memory capacities for the pages of the string. The data processing apparatus contains a first list which is a list of the names of the pages of the program and an integer associated with each page name, the integers each having one of the different discrete values of 1 to n wherein n is equal to the number of the pages in the program, the value of an integer associated with a page name being in accordance with the aforementioned LRU criterion. The novel system includes a second list and a method for utilization of such novel second list, this second list being an ordered sequence of addresses having the values of 1 to n, there being at each address an integer associated with a given page.