Algorithms and Data Structures for External Memory

148 Notations and Acronyms
lowercase notations
n = N
B
, m= M
B
Q Z
, q = , z =
B B
represent the problem size, internal memory size, query specification
size, and answer size, respectively, in units of disk blocks.
In Chapter 9, we use some modified notation to describe the problem
sizes of graph problems:
V = number of vertices; v = V
B ;
E = number of edges; e = E
B .
For simplicity, we assume that E ≥ V ; in those cases where there are
fewer edges than vertices, we set E to be V .
In the notations below, k and ℓ denote nonnegative integers and x
and y denote real-valued expressions:
Scan(N) number of I/Os to scan a file of N
(Chapter 3).
items
Sort(N) number of I/Os to sort a file of N
(Chapter 3).
items
Search(N) number of I/Os to do a dictionary lookup in a
data structure of N items (Chapter 3).
Output(Z) number of I/Os to output the Z items of the
answer (Chapter 3).
BundleSort(N,K) number of I/Os to sort a file of N items (each
with distinct secondary information) having a
total of K ≤ N unique key values (Section 5.5).
Stripe the D blocks, one on each of the D disks,
located at the same relative position on each disk
(Chapter 3).
RAM random
memory.
access memory, used for internal
DRAM dynamic random access memory, frequently used
for internal memory.