1. Coverage In Wireless Ad-Hoc Sensor Networks Shimon Tal Sion Cohen Instructor: Dr. Michael Segal

2. 2Coverage In Sensor Networs Introduction A wireless ad-hoc isotropic sensor network. Worst-Case Coverage problem. Best-Case Coverage problem. Research Goal: Sensor Networks Coverage. to define the Quality Of Service (surveillance) that can be provided by a particular sensor network.

3. 3Coverage In Sensor Networs Problem Definition: Worst Case Worst Coverage – Identify a maximal Breach Path connecting 2 locations. More Simple: Worst Coverage :=Thief. Worst-Case Path (Project’s software Screenshot)

4. 4Coverage In Sensor Networs Problem Definition: Best Case Best Coverage- Identify the maximal Support path connecting 2 locations. More Simple: More Simple: Best Coverage :=Delegation. Best-Case Path (Project’s software Screenshot)

5. 5Coverage In Sensor Networs Projects Goals 1.Algorithms’ implementation In software with Graphical Abilities (LEDA C++). 2.Improve existing algorithms for Worst- case Coverage Problem. 3.Improve existing algorithms for Best- case Coverage Problem.

6. 6Coverage In Sensor Networs Worst Coverage – Solution Domain The solution for the “ Thief ” problem must lie on the line segments of the Voronoi Diagram. The solution for the “ Thief ” problem must lie on the line segments of the Voronoi Diagram. Voronoi Diagram: In 2D,the Voronoi Diagram of a set of discrete sites (sensors) partitions the plain into a set of convex polygons such that all points inside a polygon are closest to only one site.

7. 7Coverage In Sensor Networs Voronoi Diagram Voronoi Diagram In 2D (Project’s software Screenshot)

8. 8Coverage In Sensor Networs Best Coverage – Solution Domain The solution for the “ Delegation ” problem must lie on the line segments of the Delaunay Triangulation. The Delaunay Triangulation can be obtained by connecting the sites in the Voronoi Diagram whose polygons share a common edge.

9. 9Coverage In Sensor Networs Delaunay Triangulation Delaunay Triangulation In 2D (Project’s software Screenshot)

10. 10Coverage In Sensor Networs VD & DT Together

11. 11Coverage In Sensor Networs Why Delaunay Triangulation? Proof: Empty Circle

12. 12Coverage In Sensor Networs Existing Algorithms The existing algorithm to both problems are a combination of Breadth-First-Search and Binary Search. The existing algorithm to both problems are a combination of Breadth-First-Search and Binary Search. The differences between the problems are different initialization,different graph segments (Worst-VD, Best-DT) and other minor differences.

13. 13Coverage In Sensor Networs Worst Case Existing Algorithm(1). Initialization: Initialization: 1.Range = (max_weight+min_weight)/2. 2.Breach_weight = min_weight + Range. 3.Define binary_search_tolerance. Note: binary_search_tolerance will define when the algorithm stops.

14. 14Coverage In Sensor Networs Worst Case Existing Algorithm(2). While (range > binary_search_tolerance ) While (range > binary_search_tolerance ) 1.Initialize Voronoi Diagram includes only the edges whose weight > breach_weight Named G. 2.If BFS(G,start,end) is successful breach_weight = breach_weight +range breach_weight = breach_weight +rangeElse breach_weight = breach_weight -range breach_weight = breach_weight -range 3.range=range/2.

15. 15Coverage In Sensor Networs Algorithm’s Execution

16. 16Coverage In Sensor Networs Existing Algorithm’s Disadvantages 1.Non-Stable Algorithm (edges weights dependant ). 2.The algorithm not necessarily returns the real breach weight.( Up to the BS tolerance). Trade-off between result quality/integrity and running time. (by the bs_tolarance). 3.Total High Computational complexity Dominated by the VD Construction:

17. 17Coverage In Sensor Networs Suggested Improvement: Using List instead of BS tolerance 1.First, to obtain a sorted list having all weights. 2.Perform the Binary Search on the list. This will overcome the following problems: 1.A stable algorithm. 2.Not dependent on the edges weight. 3.Gives the exact breach_weight. 4.No trade-off between quality and running time.

18. 18Coverage In Sensor Networs Another Improvement: RNG We Suggest to use in Best Coverage the Relative Neighbor Graph to construct DT in Reduced complexity in the following way: For each u,v : if edge (u,v) don’t perform empty circle then remove it. This may reduce complexity to:

19. 19Coverage In Sensor Networs Project & Code Status 1.We developed a GUI which is Algorithm independent chooses, using an OO Model. 2.The GUI enables,beside running the algorithms also VD as DT tools and other options. 3.Full Implementation of the 2 algorithms (existing & the list improvement) in both coverage problems.

20. 20Coverage In Sensor Networs Further Progress 1.Conducting tests in different scales of Sensor Networks. Collecting and analyzing the test results for comparison and evaluation of our work. 2.Develop Algorithm that reduce complexity using shortest path variant algorithm

21. 21Coverage In Sensor Networs Future Research To develop an algorithm that chooses best path among all paths according to certain criteria. for example: Smallest travelling. Observation of any point in the network is an integration of all sensors in the network.