SSS 2005 October 26 27 2005 Barcelona Spain

  • Slides: 39
Download presentation
SSS’ 2005, October 26 -27 2005, Barcelona (Spain) A Snap-Stabilizing DFS with a Lower

SSS’ 2005, October 26 -27 2005, Barcelona (Spain) A Snap-Stabilizing DFS with a Lower Space Requirement Alain Cournier, Stéphane Devismes, and Vincent Villain A Snap-Stabilizing DFS with a Lower Space Requirement

Snap-Stabilizing System? A particular class of self-stabilizing systems. (A self-stabilizing system, regardless of the

Snap-Stabilizing System? A particular class of self-stabilizing systems. (A self-stabilizing system, regardless of the initial state of the processors, is guaranteed to converge to the intended behavior in finite time. (Dijkstra 1974)) A snap-stabilizing system, regardless of the initial state of the processors, always behaves according to its specifications. (Bui et al, 1999) A Snap-Stabilizing DFS with a Lower Space Requirement 2

Model R v v Arbitrary rooted network State model – Local shared memory –

Model R v v Arbitrary rooted network State model – Local shared memory – Daemon: weakly fair/unfair A Snap-Stabilizing DFS with a Lower Space Requirement 3

Related Works Self-stabilizing area: – Huang and Chen (Distributed Computing, 1993) – Johnen and

Related Works Self-stabilizing area: – Huang and Chen (Distributed Computing, 1993) – Johnen and Beauquier (WSS, 1995) – Johnen et al (WDAG, 1997) Weakly fair Daemon – Datta et al (Distributed Computing, 2000) Snap-stabilizing area: – Cournier et al, Transformer (ICDCS, 2003) – Cournier et al (OPODIS, 2004) Unfair Daemon O(NN) states (Ids List) A Snap-Stabilizing DFS with a Lower Space Requirement 4

Write a snap-stabilizing unfair DFS protocol with a lower memory requirement (no Ids) A

Write a snap-stabilizing unfair DFS protocol with a lower memory requirement (no Ids) A Snap-Stabilizing DFS with a Lower Space Requirement 5

DFS in a non-faulty configuration R A Snap-Stabilizing DFS with a Lower Space Requirement

DFS in a non-faulty configuration R A Snap-Stabilizing DFS with a Lower Space Requirement 6

Problem of the cleaning by the leaves r nd ed it Vis A Snap-Stabilizing

Problem of the cleaning by the leaves r nd ed it Vis A Snap-Stabilizing DFS with a Lower Space Requirement e 2 h rt fo e tim 7

Problem of the cleaning by the leaves r . . . A Snap-Stabilizing DFS

Problem of the cleaning by the leaves r . . . A Snap-Stabilizing DFS with a Lower Space Requirement 8

Solution: cleaning at the end of the traversal only r A Snap-Stabilizing DFS with

Solution: cleaning at the end of the traversal only r A Snap-Stabilizing DFS with a Lower Space Requirement 9

Insuring the visit of all the processors A Snap-Stabilizing DFS with a Lower Space

Insuring the visit of all the processors A Snap-Stabilizing DFS with a Lower Space Requirement 10

Insuring the visit of all the processors r A Snap-Stabilizing DFS with a Lower

Insuring the visit of all the processors r A Snap-Stabilizing DFS with a Lower Space Requirement 11

Insuring the visit of all the processors r Processors never visited Not st p.

Insuring the visit of all the processors r Processors never visited Not st p. Sna g! lizin i b a A Snap-Stabilizing DFS with a Lower Space Requirement 12

Solution: a Question Mecanism [Blin et al, An Improved Snap-Stabilizing PIF Algorithm, 2003] Can

Solution: a Question Mecanism [Blin et al, An Improved Snap-Stabilizing PIF Algorithm, 2003] Can I switch to the red color? Only the root can deliver an answer and this answer is propagated in the spanning tree of the root only A Snap-Stabilizing DFS with a Lower Space Requirement 13

Insuring the visit of all the processors r Ok Ok A Snap-Stabilizing DFS with

Insuring the visit of all the processors r Ok Ok A Snap-Stabilizing DFS with a Lower Space Requirement 14

Insuring the visit of all the processors r Ok Ok Ok The yellow processor

Insuring the visit of all the processors r Ok Ok Ok The yellow processor waits Until the abnormal traversal disappears by Error Correction A Snap-Stabilizing DFS with a Lower Space Requirement 15

Error Correction 1 7 2 8 6 3 5 4 R A Snap-Stabilizing DFS

Error Correction 1 7 2 8 6 3 5 4 R A Snap-Stabilizing DFS with a Lower Space Requirement 16

Solution: Paralyzing Mechanism 1 2 6 3 5 4 R A Snap-Stabilizing DFS with

Solution: Paralyzing Mechanism 1 2 6 3 5 4 R A Snap-Stabilizing DFS with a Lower Space Requirement 17

Solution: Paralyzing Mechanism 1 2 6 3 5 4 R A Snap-Stabilizing DFS with

Solution: Paralyzing Mechanism 1 2 6 3 5 4 R A Snap-Stabilizing DFS with a Lower Space Requirement 18

Solution: Paralyzing Mechanism 1 2 6 3 5 4 R A Snap-Stabilizing DFS with

Solution: Paralyzing Mechanism 1 2 6 3 5 4 R A Snap-Stabilizing DFS with a Lower Space Requirement 19

Solution: Paralyzing Mechanism 1 2 6 3 5 4 R A Snap-Stabilizing DFS with

Solution: Paralyzing Mechanism 1 2 6 3 5 4 R A Snap-Stabilizing DFS with a Lower Space Requirement 20

Solution: Paralyzing Mechanism 1 2 6 3 5 4 R A Snap-Stabilizing DFS with

Solution: Paralyzing Mechanism 1 2 6 3 5 4 R A Snap-Stabilizing DFS with a Lower Space Requirement 21

Solution: Paralyzing Mechanism 1 2 6 3 5 4 R A Snap-Stabilizing DFS with

Solution: Paralyzing Mechanism 1 2 6 3 5 4 R A Snap-Stabilizing DFS with a Lower Space Requirement 22

Solution: Paralyzing Mechanism 1 2 6 3 5 4 R A Snap-Stabilizing DFS with

Solution: Paralyzing Mechanism 1 2 6 3 5 4 R A Snap-Stabilizing DFS with a Lower Space Requirement 23

Solution: Paralyzing Mechanism 1 2 6 3 5 4 R A Snap-Stabilizing DFS with

Solution: Paralyzing Mechanism 1 2 6 3 5 4 R A Snap-Stabilizing DFS with a Lower Space Requirement 24

Solution: Paralyzing Mechanism 1 2 6 3 5 4 R A Snap-Stabilizing DFS with

Solution: Paralyzing Mechanism 1 2 6 3 5 4 R A Snap-Stabilizing DFS with a Lower Space Requirement 25

Solution: Paralyzing Mechanism 1 2 6 3 5 4 R A Snap-Stabilizing DFS with

Solution: Paralyzing Mechanism 1 2 6 3 5 4 R A Snap-Stabilizing DFS with a Lower Space Requirement 26

Solution: Paralyzing Mechanism 1 2 6 3 5 4 R A Snap-Stabilizing DFS with

Solution: Paralyzing Mechanism 1 2 6 3 5 4 R A Snap-Stabilizing DFS with a Lower Space Requirement 27

Solution: Paralyzing Mechanism 1 2 6 3 5 4 R A Snap-Stabilizing DFS with

Solution: Paralyzing Mechanism 1 2 6 3 5 4 R A Snap-Stabilizing DFS with a Lower Space Requirement 28

Solution: Paralyzing Mechanism 1 2 6 3 5 4 R A Snap-Stabilizing DFS with

Solution: Paralyzing Mechanism 1 2 6 3 5 4 R A Snap-Stabilizing DFS with a Lower Space Requirement 29

Solution: Paralyzing Mechanism 2 6 3 5 4 R A Snap-Stabilizing DFS with a

Solution: Paralyzing Mechanism 2 6 3 5 4 R A Snap-Stabilizing DFS with a Lower Space Requirement 30

Solution: Paralyzing Mechanism 6 3 5 4 R A Snap-Stabilizing DFS with a Lower

Solution: Paralyzing Mechanism 6 3 5 4 R A Snap-Stabilizing DFS with a Lower Space Requirement 31

Solution: Paralyzing Mechanism 6 5 R 4 A Snap-Stabilizing DFS with a Lower Space

Solution: Paralyzing Mechanism 6 5 R 4 A Snap-Stabilizing DFS with a Lower Space Requirement 32

Solution: Paralyzing Mechanism 6 R 5 A Snap-Stabilizing DFS with a Lower Space Requirement

Solution: Paralyzing Mechanism 6 R 5 A Snap-Stabilizing DFS with a Lower Space Requirement 33

Solution: Paralyzing Mechanism 6 R A Snap-Stabilizing DFS with a Lower Space Requirement 34

Solution: Paralyzing Mechanism 6 R A Snap-Stabilizing DFS with a Lower Space Requirement 34

Solution: Paralyzing Mechanism R A Snap-Stabilizing DFS with a Lower Space Requirement 35

Solution: Paralyzing Mechanism R A Snap-Stabilizing DFS with a Lower Space Requirement 35

Conclusion v Snap-Stabilizing v Arbitrary Rooted Networks v Unfair Daemon A Snap-Stabilizing DFS with

Conclusion v Snap-Stabilizing v Arbitrary Rooted Networks v Unfair Daemon A Snap-Stabilizing DFS with a Lower Space Requirement 36

Conclusion: SSS’ 05 vs OPODIS’ 04 SSS’ 05 O(NN) O(∆²× N) Yes No 0

Conclusion: SSS’ 05 vs OPODIS’ 04 SSS’ 05 O(NN) O(∆²× N) Yes No 0 0 Delay (rounds) O(N²) Delay (steps) O(N²) O(N 3) Execution (rounds) O(N²) Execution (steps) O(N²) O(N 3) Memory Requirement Ids Stabilization time A Snap-Stabilizing DFS with a Lower Space Requirement 37

Perspective Finding an efficient solution in both time and space complexities A Snap-Stabilizing DFS

Perspective Finding an efficient solution in both time and space complexities A Snap-Stabilizing DFS with a Lower Space Requirement 38

Thank You! A Snap-Stabilizing DFS with a Lower Space Requirement 39

Thank You! A Snap-Stabilizing DFS with a Lower Space Requirement 39