Brief Announcement: Sorting on Skip Chains Ajoy K. Datta, Lawrence L. Larmore, and Stéphane Devismes.

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Presentation transcript:

Brief Announcement: Sorting on Skip Chains Ajoy K. Datta, Lawrence L. Larmore, and Stéphane Devismes

Skip Chain October, 11, 2011SSS'2011, Grenoble2 Left Right Major nodes Relay nodes

Skip Chain Sorting October, 11, 2011SSS'2011, Grenoble

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, 2011SSS'2011, Grenoble4

Overview Idea : distributed bubble sort October, 11, 2011SSS'2011, Grenoble5 Arbitrary Configurations Normal Configurations Legitimate Configurations Error Correction Sorting

Data Structure October, 11, 2011SSS'2011, Grenoble

Swap October, 11, 2011SSS'2011, Grenoble Synchronization between swaps : 4 colors

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 color October, 11, 2011SSS'2011, Grenoble8

Example October, 11, 2011SSS'2011, Grenoble9 X Yz Compare and swap V(y)V(x)

Example October, 11, 2011SSS'2011, Grenoble10 X Yz V(y)’V(x)’ 0, V(x)’1, V(y)’

Example October, 11, 2011SSS'2011, Grenoble11 X Yz Compare and swap V(y)’V(x)’ V(y)’ V(u) V(x)’

Example October, 11, 2011SSS'2011, Grenoble12 X Yz Compare and swap V(y)’V(x)’ V(x)’’ V(y)’ V(u)’ 2 1, V(x)’’

Example October, 11, 2011SSS'2011, Grenoble13 X Yz V(y)’V(x)’’ V(y)’ V(u)’

Example October, 11, 2011SSS'2011, Grenoble14 X Yz V(y)’V(x)’’ V(y)’ V(u)’ 2 3

Example October, 11, 2011SSS'2011, Grenoble15 X Yz V(y)’V(x)’’ V(y)’ V(u)’

Example October, 11, 2011SSS'2011, Grenoble16 X Yz V(y)’V(x)’’ V(y)’ V(z) V(u)’ Compare and swap

Example October, 11, 2011SSS'2011, Grenoble17 X Yz V(y)’V(x)’’ V(y)’’ V(z)’ V(u)’ 0, V(y)’’ 3

Example October, 11, 2011SSS'2011, Grenoble18 X Yz V(y)’’V(x)’’ V(y)’’ V(z)’ V(u)’

Example October, 11, 2011SSS'2011, Grenoble19 X Yz V(y)’’V(x)’’ V(y)’’ V(z)’ V(u)’

Error correction October, 11, 2011SSS'2011, Grenoble20

Silence October, 11, 2011SSS'2011, Grenoble Done

Perspective Can we enhance the round complexity to O(n) rounds ? Step complexity ? October, 11, 2011SSS'2011, Grenoble22

Thank you October, 11, 2011SSS'2011, Grenoble23

Min-Max Search Tree October, 11, 2011SSS'2011, Grenoble <= 3 3 min max