Algorithms and Data Structures for External Memory

2.1 PDM and Problem Parameters 11
use block transfer. Figure 1.1 depicts typical memory sizes and block
sizes for various levels of memory.
Because I/O is done in units of blocks, algorithms can run considerably
faster when the pattern of memory accesses exhibit locality
of reference as opposed to a uniformly random distribution. However,
even if an application can structure its pattern of memory accesses and
exploit locality, there is still a substantial access gap between internal
and external memory performance. In fact the access gap is growing,
since the latency and bandwidth of memory chips are improving more
quickly than those of disks. Use of parallel processors (or multicores)
further widens the gap. As a result, storage systems such as RAID
deploy multiple disks that can be accessed in parallel in order to get
additional bandwidth [101, 194].
In the next section, we describe the high-level parallel disk model
(PDM), which we use throughout this manuscript for the design and
analysis of EM algorithms and data structures. In Section 2.2, we consider
some practical modeling issues dealing with the sizes of blocks and
tracks and the corresponding parameter values in PDM. In Section 2.3,
we review the historical development of models of I/O and hierarchical
memory.
2.1 PDM and Problem Parameters
We can capture the main properties of magnetic disks and multiple disk
systems by the commonly used parallel disk model (PDM) introduced
by Vitter and Shriver [345]. The two key mechanisms for efficient algorithm
design in PDM are locality of reference (which takes advantage
of block transfer) and parallel disk access (which takes advantage of
multiple disks). In a single I/O, each of the D disks can simultaneously
transfer a block of B contiguous data items.
PDM uses the following main parameters:
N = problem size (in units of data items);
M = internal memory size (in units of data items);
B = block transfer size (in units of data items);