Brief Announcement: Sorting on Skip Chains
24
Brief Announcement: Sorting on Skip Chains Ajoy K. Datta, Lawrence L. Larmore, and Stéphane Devismes
description
Brief Announcement: Sorting on Skip Chains. Ajoy K. Datta , Lawrence L. Larmore , and Stéphane Devismes. Skip Chain. Major nodes. Left. Right. Relay nodes. Skip Chain Sorting. 3. 6. 2. 2. 3. 6. Contribution. Skip Chain Sorting Algorithm Self-stabilizing Silent - PowerPoint PPT Presentation
Transcript of Brief Announcement: Sorting on Skip Chains
Brief Announcement: Sorting on Skip Chains
Ajoy K. Datta, Lawrence L. Larmore, and Stéphane Devismes
SSS'2011, Grenoble 2
Skip Chain
October, 11, 2011
Left Right
Major nodes
Relay nodes
SSS'2011, Grenoble 3
Skip Chain Sorting
October, 11, 2011
3 6 2
2 3 6
SSS'2011, Grenoble 4
Contribution
• Skip Chain Sorting Algorithm– Self-stabilizing– Silent– Locally shared memory model
• Unfair demon• O(b) space, b = number of bits to encode a value• O(md) rounds
– m : number of major nodes– d : maximum number of relay between two major nodes– md = O(n) if the spacing between major processes is roughtly equal
October, 11, 2011
SSS'2011, Grenoble 5
Overview
• Idea : distributed bubble sort
October, 11, 2011
Arbitrary Configurations
Normal Configurations
Legitimate Configurations
Error Correction
Sorting
SSS'2011, Grenoble 6
Data Structure
October, 11, 2011
3 26
SSS'2011, Grenoble 7
Swap
October, 11, 2011
26
6 6 6 266
2 2 2 622
Synchronization between swaps : 4 colors
SSS'2011, Grenoble 8
Colors
• A value moves to the left at the crest of wave 0
• A value moves to the right at the crest of wave 1
• Colors 2 and 3 to avoid ambiguïty and to synchronize
• Color E: error colorOctober, 11, 2011
SSS'2011, Grenoble 9
Example
October, 11, 2011
X Y z
33 03 20
Compare and swap
V(y)V(x)
SSS'2011, Grenoble 10
Example
October, 11, 2011
X Y z
33 10 20
V(y)’V(x)’
0, V(x)’ 1, V(y)’
SSS'2011, Grenoble 11
Example
October, 11, 2011
X Y z
03 10 21
Compare and swap
V(y)’V(x)’ V(y)’V(u) V(x)’
SSS'2011, Grenoble 12
Example
October, 11, 2011
X Y z
10 10 32
Compare and swap
V(y)’V(x)’V(x)’’ V(y)’V(u)’
21, V(x)’’
SSS'2011, Grenoble 13
Example
October, 11, 2011
X Y z
10 21 32
V(y)’V(x)’’V(x)’’ V(y)’V(u)’
SSS'2011, Grenoble 14
Example
October, 11, 2011
X Y z
10 32 32
V(y)’V(x)’’V(x)’’ V(y)’V(u)’
2 3
SSS'2011, Grenoble 15
Example
October, 11, 2011
X Y z
20 32 33
V(y)’V(x)’’V(x)’’ V(y)’V(u)’
SSS'2011, Grenoble 16
Example
October, 11, 2011
X Y z
21 32 03
V(y)’V(x)’’V(x)’’ V(y)’ V(z)V(u)’Compare and swap
SSS'2011, Grenoble 17
Example
October, 11, 2011
X Y z
32 32 10
V(y)’V(x)’’V(x)’’ V(y)’’ V(z)’V(u)’
0, V(y)’’ 3
SSS'2011, Grenoble 18
Example
October, 11, 2011
X Y z
32 03 10
V(y)’’V(x)’’V(x)’’ V(y)’’ V(z)’V(u)’
SSS'2011, Grenoble 19
Example
October, 11, 2011
X Y z
33 03 20
V(y)’’V(x)’’V(x)’’ V(y)’’ V(z)’V(u)’
SSS'2011, Grenoble 20
Error correction
October, 11, 2011
SSS'2011, Grenoble 21
Silence
October, 11, 2011
2 2 3 3 3 3 62 32
Done
SSS'2011, Grenoble 22
Perspective
• Can we enhance the round complexity to O(n) rounds ?
• Step complexity ?
October, 11, 2011
SSS'2011, Grenoble 23
Thank youOctober, 11, 2011
SSS'2011, Grenoble 24
Min-Max Search Tree
October, 11, 2011
10
1
95
84 7
62
<= <=
3<=
min
min
max
max
