Block swap algorithms: Difference between revisions

Content deleted Content added

Inline

Revision as of 13:31, 5 November 2021

In computer algorithms, Block swap algorithms swap two regions of elements of an array. It is simple to swap two non-overlapping regions of an array of equal size. However, it is not simple to swap two non-overlapping regions of an array in-place that are next to each other, but are of unequal sizes. Three algorithms are known to accomplish this: Bentley's Juggling (also known as Dolphin Algorithm ^[1]), Gries-Mills, and Reversal.^[2] All three algorithms are linear time O(n), (see Time complexity).

Reversal algorithm

The reversal algorithm is the simplest to explain, using rotations. A rotation is an in-place reversal of array elements. This method swaps two elements of an array from outside in within a range. The rotation works for an even number of elements or an odd number of array elements. The reversal algorithm uses three in-place rotations to accomplish an in-place block swap:

Rotate region A
Rotate region B
Rotate region AB

Gries-Mills and Reversal algorithms perform better than Bentley's Juggling, because of their cache-friendly memory access pattern behavior.

The Reversal algorithm parallelizes well, because rotations can be split into sub-regions, which can be rotated independently of others.

References

^ D. Gries, H. Mills (1981), Swapping Sections
^ Jon Bentley, "Programming Pearls", pp. 13–15, 209-211.

[1] D. Gries, H. Mills (1981), Swapping Sections

[2] Jon Bentley, "Programming Pearls", pp. 13–15, 209-211.

[1]

[2]

@@ Line 1: / Line 1: @@
 {{Context|date=July 2019}}
-'''Block swap algorithms'''  swap two elements of an [[Array data structure|array]] in computer [[algorithm]]s. It is simple to swap two non-overlapping regions of an [[array data structure|array]] of equal size. However, it is not simple to swap two non-overlapping regions of an array in-place that are next to each other, but are of unequal sizes. Three algorithms are known to accomplish this: Bentley's Juggling, Gries-Mills, and Reversal.<ref>Jon Bentley, "Programming Pearls", pp. 13–15, 209-211.</ref> All three algorithms are linear time [[Big O notation|
+In computer [[algorithm]]s, '''Block swap algorithms''' swap two regions of elements of an [[Array data structure|array]]. It is simple to swap two non-overlapping regions of an [[array data structure|array]] of equal size. However, it is not simple to swap two non-overlapping regions of an array in-place that are next to each other, but are of unequal sizes. Three algorithms are known to accomplish this: Bentley's Juggling (also known as ''Dolphin Algorithm'' <ref>D. Gries, H. Mills (1981), [https://hdl.handle.net/1813/6292 Swapping Sections]</ref>), Gries-Mills, and Reversal.<ref>Jon Bentley, "Programming Pearls", pp. 13–15, 209-211.</ref> All three algorithms are linear time [[Big O notation|
 O(n)]], (see [[Time complexity]]).