1. Greedy Distributed Spanning tree routing (gdstr)
Cmpe 259: Sensor Networks
MATTHEW HENDRICKS

2. WIRELESS SENSOR NETWORKS
Requirements:
Made up of several nodes/sensors
Nodes consist of a CPU, storage, transmitter, and battery
Communications sometimes take many hops to reach the sink

3. Scalability of sensor networks
  Limited recourses lead design
Battery powered
Less storage
Scalability and Robustness
Must accommodate additional nodes
Has to work though node failure

4. Mica 2 "mote" Price (about $150) Sensor expantion board ($120) - light
        - temperature
        - microphone
More sofisticated boards available
        - accelerometers
        - GPS    

5. Dynamic Topologies Node issues Nodes are subject to physical harm
Hardware issues
Battery failure
Transmission issues
Physical obstacles
RF interference 

6. Packet destination field = the destination location
The approach of GDSTR 
     Route via location
Nodes are aware of their location
GPS
Static location
Indoor networks
             Packet destination field = the destination location

7. Prerequisites of gDTSr
Node placement occur on a plane Radio Links are Bi-Directional Transmission power is uniform

8. Geographic routing Greedy forwarding: Uses local information to route
Hop closest to destination  is chosen

9. Issues Dead ends Closest neighbor to destination not always available
Face routing remedy used in other protocols 

10. Face routing
Route messages through planar graph
Does not scale well

11. Hull trees Each node has a "convex hull"
Convex hulls contain all  descendant nodes within
Storage is O(1) vs. O(N)

12. Routing with hull trees
If destination is not within convex hull, forward to the parent
If destination is in the convex hull, forward packet 

13. Routing with hull trees continued...
           If the packet was in greedy mode previously or was sent from the parent node:
Packet will be forwarded to first child node containing destination. 
If the packet came from a child node:
Packet will be forwarded to the next child node that's convex has the destination within it
If the packet came from child node from hulls that have destination within:
Packet will go to the parent or child node that is also root node.

14. PERFORMANCE ISSUES
Routing via decisions based on trees is slower
GDSTR only uses trees when needed
GDSTR switches back to greedy routing as soon as possible
Tree hops are used as little as possible

15. Creation of hull trees
Routing performance gains from less overlap between convex hulls
Compact trees are ideal and lead to less  hop count
Smaller trees broadcast chosen parent node and convex hull 

16. Routing algorithm Mode: current greedy or tree routing style
N min: node where packet switches from greedy to tree routing 
Tree: identifier for the root of hull tree
N anchor: first discovered node while traversing tree

17. Algorithm (GDSTR) Check for Greedy mode switch Greedy Mode Tree Mode
Choose Hull Tree
Check Hull Tree
Not in Hull Tree
Check Anchor Node
Termination Condition
Tree Traversal 

18. 1. Checking for mode
"If p.mode = Tree and there is at least one immediate neighbor w such that |wt| < |(p.nmin)t|, then set p.mode := Greedy, p.nmin := w and clear p.nanchor and p.tree if they are set. Execute step 2 or 3 according to p.mode"

19. 2. Greedy Mode
Find the node w in the set of immediate neighbors that is closest to t. If |wt| < |vt|, forward the packet to w. Otherwise, set p.mode := Tree and follow step 3.

20. 3. Tree Mode
If p.tree is not set or if the root for p.tree has changed, follow step 4, else follow step 5.

21. 4. Choose Hull Tree
Choose one of the existing hull trees for forwarding and set p.tree to the chosen tree’s identifier. Follow step 5.

22. 5. Check Hull Tree
If hull tree does not contain destination node t, follow step 6; otherwise, follow step 7 instead.

23. 6. Not in Hull Tree
If none of the hulls in H contains the destination node t conclude that the packet is not deliverable. Otherwise, forward p to the parent node in p.tree.

24. 7. Check Anchor Node
If p.nanchor is set, follow step 8. Else, set p.nanchor := v and follow step 9 instead.

25. 8. Termination Condition
Given a global ordering for node identifiers, arrange the child nodes (relative to p.tree) with convex hulls that contain the destination point in a ascending sequence according to the global ordering. Then: 5 If v = p.anchor and either (i) u is the last child and v is the root node for p.tree, (ii) u is the last child and the set of conflict hulls H does not contain destination node t, or (iii) u is the parent node, conclude that packet is not deliverable; else If u is the parent node and the set of conflict hulls H does not contain destination node t, set p.nanchor := v. Follow step 9. "

26. 9. Tree Traversal
If p.mode = Greedy set p.mode := Tree, forward packet to the first child node; If packet was received from the parent node forward packet to the first child node; If packet was received from a child node forward packet to the next child node in the sequence; If packet was received from the last child node if one of the hulls in H contains the destination point; forward packet to the parent node Else forward packet to the first child node.

27. Simulation Unit radio range
    Communication if and only if within range, and have line of site
Wireless issues not accounted for
Networks of 25 to 500 nodes
    Randomly place in 10 x 10 unit square
200 networks tested
    20,000 packets routed
    Source and destination randomly selected

28. Simulation comparisons
Greedy Perimeter Stateless Routing (GPSR)
Greedy Other Adaptive Face Routing Plus (GOAFR+)
Greedy Path Vector Face Routing (GPVFR)
Cross-Link Detection Protocol (CLDP) planarization
A density of 500 nodes in 100 square units is high enough that greedy forwarding almost always succeeds

29. Routing Results Path stretch: Ratio of path length between nodes
Hop stretch: ratio of hops between two nodes against the number of hops on the shortest path
Metrics were considered similar enough to be plotted together

30. Routing results
From node degree range 2 to 9 GDSTR outperforms other algorithms
Most improvement in the node degree range 4 to 6
GDSTR routes where often shorter
        Faster delivery
        Less consumption of radio resources

31. Bandwidth Results GDSTR broadcast (keep alive) vs. CLDP probes
Broadcast messaging smaller on average up till a node degree of 4 to 8
Probes contain all point faces
4 to 8 range had largest perimeters 

32. Bandwidth results
CLDP probes are sent out until all links are considered dormant or non-routable
GDSTR converges when hull information stabalizes 

33. Scalability results CLDP message count independent of node count
GDSTR fail messaging increases gradually with node count
GDSTR join messaging independent of node count

34. conclusions
Hull trees can be at least as efficient as planar graphs after greedy forwarding
GDSTR uses less maintenance bandwidth than CLDP
Testing was conducted on stationary two dimensional graphs, but could adapt to mobile multidimensional situation