Reading data in a hierarchical memory

In 1987 A Aggarwal, A.K. Chandra and M. Snir developed a model of hierarchical memory with block transfer. It is an extension of the common RAM-model, where access to location x takes time f(x) and copying of memory blocks is supported. In the present paper this hierarchical memory model is specified by assuming f to be a nondecreasing step function, which comes closer to real architectures of hierarchical memories. An algorithm for reading large files is proposed and its optimality proved.