Affiliation:
1. Univ. of Illinois, Urbana
Abstract
Consider two linearly ordered sets
A, B
, |
A
| =
m
, |
B
| =
n, m
≤
n
, and
p, p
≤
m
, parallel processors working synchronously. The paper presents an algorithm for merging
A
and
B
with the
p
parallel processors, which requires at most 2⌈log
2
(2
m
+ 1)⌉ + ⌊3
m
/
p
⌋ + [
m
/
p
][log
2
(
n
/
m
)] steps. If
n
= 2
β
m
(
β
an integer), the algorithm requires at most 2[log
2
(
m
+ 1)] + [
m
/
p
](2 +
β
) steps. In the case where
m
and
n
are of the same order of magnitude, i.e.
n
=
km
with
k
being a constant, the algorithm requires 2[log
2
(
m
+ 1)] + [
m
/
p
](3 +
k
) steps. These performances compare very favorably with the previous best parallel merging algorithm, Batcher's algorithm, which requires
n
/
p
+ ((
m
+
n
)/2
p
)log
2
m
steps in the general case and
km
/
p
+ ((
k
+ 1)/2)(
m
/
p
)log
2
m
in the special case where
n
=
km
.
Publisher
Association for Computing Machinery (ACM)
Cited by
22 articles.
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