Algorithms and Data Structures for External Memory

50 External Sorting and Related Problems
Output buffers /
Input buffers
Merging buffers /
Partitioning buffers
Prefetch buffers /
Output buffers
1 2 3 4 5
R = 8 runs / S = 8 buckets
D = 6 Disks
1 2 3 4
5
6
7 8
1 2 3 4 5 6
D = 6 Disks
6
Up to 3-D
I/O-buffered
blocks
Disk numbers
Blocks disassembled
via merge
Blocks assembled
via distribution
Stream of blocks are
read in Σ order
Stream of blocks are
written in Σ order
R
Up to m’
prefetched or
queued blocks
D = 6
Disk numbers
Correspondence between
output step in greedy write-once schedule
and prefetching step in lazy read-once schedule
Fig. 5.8 Duality between merging with R = 8 runs and distribution with S = 8 buckets,
using D = 6 disks. The merge of the R runs proceeds from bottom to top. Blocks are input
from the disks, stored in the prefetch buffers, and ultimately read into the merging buffers.
The blocks of the merged run are moved to the output buffers and then output to the disks.
The order in which blocks enter the merging buffers determines the sequence Σ, which
can be predetermined by ordering the blocks based upon their smallest key values. The
distribution into S buckets proceeds from top to bottom. Blocks are input from the disks
into input buffers and moved to the partitioning buffers. The blocks of the resulting buckets
are written in the order Σ R to the output buffers and then output to the appropriate disks.
Internal Memory