1 / 39

A Snap-Stabilizing DFS with a Lower Space Requirement

This paper introduces a snap-stabilizing DFS (Depth-First Search) protocol with a lower memory requirement. It guarantees convergence to the intended behavior in finite time. The protocol is designed for arbitrary rooted networks and uses a state model and local shared memory.

kimsey
Download Presentation

A Snap-Stabilizing DFS with a Lower Space Requirement

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

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

  2. 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

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

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

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

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

  7. Visited for the 2nd time Problem of the cleaning by the leaves r A Snap-Stabilizing DFS with a Lower Space Requirement

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

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

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

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

  12. Insuring the visit of all the processors Processors never visited r Not Snap-stabilizing! A Snap-Stabilizing DFS with a Lower Space Requirement

  13. 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

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

  15. 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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

  37. Conclusion: SSS’05 vs OPODIS’04 A Snap-Stabilizing DFS with a Lower Space Requirement

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

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

More Related