1. GS 3 GS 3 : Scalable Self-configuration and Self-healing in Wireless Networks Hongwei Zhang & Anish Arora

2. Introduction Sensor networks are not deployed manually  self-configuration (into interconnected clusters) Sensor nodes and wireless links are subject to a rich class of faults  self-healing (of clusters and interconnections) Sensor networks need to scale well in time, space, and resources  scalability in self-configuration and self-healing

3. Scalability via locality An ideal goal for locality : self-healing should be a function of the size of perturbation (in time, space, and energy) Example: problem of dining philosophers for correctness: dining philosophers need “information” only from philosophers at distance ≤ 2 hops for fault-tolerance: (Nesterenko and Arora’02) if state corruptions occur within a 2-hop neighborhood, they can be corrected within the neighborhood itself any number of Byzantine philosophers can be tolerated as long as they are ≥ 2 hops away

4. Locality via choice of model Locality for some graph problems is hard e.g. self-configuration and self-healing of routing tree Our approach to simplifying design of locality choose a proper model for specific problems

5. System model System multiple “small” nodes and one “big” node, on a plane node distribution density: (  R t s.t. with high probability, there are multiple nodes in any circular area of radius R t ) localization: relative location between nodes can be estimated Perturbations dynamic nodes joins, leaves (deaths), state corruptions mobile nodes

6. Geography-aware self-configuration Geographic radius of clusters is crucial for communication quality, energy dissipation, data aggregations & applications Problem statement Given R: ideal cell radius (R > R t ) Construct a set of cells, connected via a “head” node in each cell s.t. radius of each cell is in [ R-c, R+c ], where c = f (R t ) each node belongs to only one cell cells and the connectivity graph over head nodes self-heal locally

7. Outline Static networks Dynamic networks Mobile dynamic networks Related work Conclusions

8. Static networks An ideal case: In reality: no node may exist at some geometric centers (ILs), but, with high probability there are nodes no more than R t away from any IL (IL = Ideal Location)

9. How to find the set of cell heads Bottom-up ? hard to guarantee the placement and size of clusters Top-down w.r.t. big node use diffusing computation but, accumulation in deviation of head location from IL is a problem i

10. Organizing neighboring clusters & heads Deviation problem is handled locally instead of using real locations, node i uses its and its parent’s ILs i calculates the ILs of next band cells in its search region big node: other nodes:, where a  Sin -1 (R t / R) for each IL, i ranks nodes within R t radius of the IL (by ), and selects the highest ranked node as the corresponding cluster head

11. Summary: static networks Cell structure is hexagonal cell radius: Time taken to form the structure is  (D b ), where D b = the maximum distance between the big node and the small nodes Scalability in self-configuration: local coordination: only with nodes within range local knowledge: each node maintains info about a constant number of nearby nodes

12. Outline Static networks Dynamic networks Mobile dynamic networks Related work Conclusions

13. Dynamic networks Dynamics include: node join, leave (death), state corruption Common vs. rare common perturbations: node density is preserved rare perturbations: node density is destroyed Scalable self-healing is achieved via locality in: intra-cell healing inter-cell healing sanity checking of state (invariants)

14. Local intra-cell healing Head shift upon head leaving (death) local in a radius of R t Cell shift upon the death of all the nodes in an area of radius R t local in a radius of R independent but consistent shift at individual cells  sliding of the global head level structure

15. H0H0 H0H0 H0H0 H0H0

16. Local inter-cell healing & sanity checking Local inter-cell healing : upon failure of intra-cell healing at head j, first, the parent of j tries to find a new head j’ if that fails, the children of j find new parents Local sanity checking of state invariants : upon detecting violation of the hexagonality property, node corrects itself after checking with its neighbors when state perturbation includes several nodes, the perturbed region corrects itself from the outside going in, and all nodes are corrected within time proportional to size of perturbed region

17. Summary: dynamic networks Cell radius for cells not adjoining any gap: for cells adjoining a gap: Head tree is now minimum distance tree rooted at the big node Stabilization time from perturbed state:  (D p ), where D p = diameter of the continuously perturbed area

18. Summary: dynamic networks (contd.) Scalability in self-healing: local fault-containment and healing local knowledge Local healing and fault-containment enables stable cell structure lengthened lifetime:  (n c ), where n c = the number of nodes in a cell

19. Outline Static networks Dynamic networks Mobile dynamic networks Related work Conclusions

20. Mobile dynamic networks H0H0 d

21. Outline Static networks Dynamic networks Mobile dynamic networks Related work Conclusions

22. Related work Cellular hexagon structure (Mac Donald ’79) Preconfigured & not considering self-healing LEACH (Heinzelman et al ’00) No guarantee about the placement and size of clusters Perturbations dealt with by globally repeating the whole clustering process

23. Related work (contd.) Logical-radius based clustering (in Banerjee ’ 01) non-local cluster maintenance, and no consideration of state corruption only logical radius  long links and link asymmetry are possible multiple rounds of diffusion Self-stabilization tree maintenance (in Arora & Gouda ’90) not fault containing local mending (in Kutten & Peleg ’95) local in time, not in space

24. Outline Static networks Dynamic networks Mobile dynamic networks Related work Conclusions

25. GS 3 is scalable self-configuration self-healing And this is achieved by exploiting the model properties in wireless sensor networks Density Localization (Note: we have also designed an algorithm for “local containment of faults in general spanning trees” for dynamic networks)