1. Hannes Frey, Ivan Stojmenovic MobiCom 2006
On Delivery Guarantees of Face and Combined Greedy-Face Routing in Ad Hoc and Sensor Networks
Hannes Frey, Ivan Stojmenovic
MobiCom 2006

2. Face Recovery Details When to change current face traversal?
How to decide the next face locally?

3. Example 1
Greedy Perimeter Stateless Routing GPSR [Karp, Kung, 2000]

4. GPSR – The FACE Routing Part
“On each face, the traversal uses the right hand rule to reach an edge that crosses line xT. At that edge, the traversal moves to the adjacent face crossed by xT. … The node forwards the packet along the first edge of this next face – by applying the right hand rule, …” [Karp & Kung 2000]

5. GPSR – The FACE Routing Partx V
“On each face, the traversal uses the right hand rule to reach an edge that crosses line xT. At that edge, the traversal moves to the adjacent face crossed by xT. … The node forwards the packet along the first edge of this next face – by applying the right hand rule, …” [Karp & Kung 2000]

6. GPSR – The FACE Routing Partx F1 F2 V
“On each face, the traversal uses the right hand rule to reach an edge that crosses line xT. At that edge, the traversal moves to the adjacent face crossed by xT. … The node forwards the packet along the first edge of this next face – by applying the right hand rule, …” [Karp & Kung 2000]

7. GPSR – The FACE Routing Partx V
“On each face, the traversal uses the right hand rule to reach an edge that crosses line xT. At that edge, the traversal moves to the adjacent face crossed by xT. … The node forwards the packet along the first edge of this next face – by applying the right hand rule, …” [Karp & Kung 2000]

8. GPSR – The FACE Routing Partx V
“On each face, the traversal uses the right hand rule to reach an edge that crosses line xT. At that edge, the traversal moves to the adjacent face crossed by xT. … The node forwards the packet along the first edge of this next face – by applying the right hand rule, …” [Karp & Kung 2000]

9. GPSR – The FACE Routing Partx
“On each face, the traversal uses the right hand rule to reach an edge that crosses line xT. At that edge, the traversal moves to the adjacent face crossed by xT. … The node forwards the packet along the first edge of this next face – by applying the right hand rule, …” [Karp & Kung 2000]

10. What about Delivery Guarantees?C E

11. What about Delivery Guarantees?C E
Outer Face

12. What about Delivery Guarantees?C E
Outer Face

13. What about Delivery Guarantees?C E

14. What about Delivery Guarantees?x B S T D C E
GPSR Forwarding Loop for GG, RNG, and LDT

15. Is this an Issue for Greedy + PSR?Q F2 E B C
[Kim et al., 2005] D

16. Example 2
Greedy-Face-Greedy GFG, [Bose et al., 1999]

17. GFG – The face routing partS T F
P  S
repeat
Let F be the face with P on boundary and intersecting PT
Traverse* F until reaching an edge that intersects PT at some point Q≠P
P  Q
until P=T
*counterclockwise if inner, clockwise if outer face

18. GFG – The face routing partQ P S T F
P  S
repeat
Let F be the face with P on boundary and intersecting PT
Traverse* F until reaching an edge that intersects PT at some point Q≠P
P  Q
until P=T
*counterclockwise if inner, clockwise if outer face

19. GFG – The face routing partS T F
P  S
repeat
Let F be the face with P on boundary and intersecting PT
Traverse* F until reaching an edge that intersects PT at some point Q≠P
P  Q
until P=T
*counterclockwise if inner, clockwise if outer face

20. GFG – The face routing partS T F
P  S
repeat
Let F be the face with P on boundary and intersecting PT
Traverse* F until reaching an edge that intersects PT at some point Q≠P
P  Q
until P=T
*counterclockwise if inner, clockwise if outer face

21. What about the GPSR Loop?D C E
Outer Face

22. What about the GPSR Loop?D C E
Outer Face

23. What about the GPSR Loop?
Select face with P on boundary and intersecting PT A B S T D C E P
Outer Face

24. What about the GPSR Loop?D C E
Outer Face

25. Observation Difference between GPSR and GFG
GFG might stay in the same face after an intersection was encountered
GPSR always changes to the next face
However, does GFG provide guaranteed delivery?

26. Example 3
Greedy Path Vector Face Routing (GPVFR) [Leong, Mitra, Liskov, 2005]

27. GPVFR – The Face Routing PartS T F B
1. Find the face F containing the line segment ST. Let A and B be the clockwise and anti-clockwise nodes. If |AT| ≤ |BT|, forward the packet clockwise along F; if |AT| > |BT|, forward the packet anti-clockwise.
2. If any adjacent edge intersects the line segment ST then set S to current node C and go to step 1. [Leong, Mitra, Liskov, 2005]

28. GPVFR – The Face Routing PartS T B
1. Find the face F containing the line segment ST. Let A and B be the clockwise and anti-clockwise nodes. If |AT| ≤ |BT|, forward the packet clockwise along F; if |AT| > |BT|, forward the packet anti-clockwise.
2. If any adjacent edge intersects the line segment ST then set S to current node C and go to step 1. [Leong, Mitra, Liskov, 2005]

29. GPVFR – The Face Routing Part
S := C A C S T B
1. Find the face F containing the line segment ST. Let A and B be the clockwise and anti-clockwise nodes. If |AT| ≤ |BT|, forward the packet clockwise along F; if |AT| > |BT|, forward the packet anti-clockwise.
2. If any adjacent edge intersects the line segment ST then set S to current node C and go to step 1. [Leong, Mitra, Liskov, 2005]

30. GPVFR – The Face Routing PartS S T F B
1. Find the face F containing the line segment ST. Let A and B be the clockwise and anti-clockwise nodes. If |AT| ≤ |BT|, forward the packet clockwise along F; if |AT| > |BT|, forward the packet anti-clockwise.
2. If any adjacent edge intersects the line segment ST then set S to current node C and go to step 1. [Leong, Mitra, Liskov, 2005]

31. GPVFR – The Face Routing PartS S T B
1. Find the face F containing the line segment ST. Let A and B be the clockwise and anti-clockwise nodes. If |AT| ≤ |BT|, forward the packet clockwise along F; if |AT| > |BT|, forward the packet anti-clockwise.
2. If any adjacent edge intersects the line segment ST then set S to current node C and go to step 1. [Leong, Mitra, Liskov, 2005]

32. What about Delivery Guarantees?

33. What about Delivery Guarantees?F T B

34. What about Delivery Guarantees?C

35. What about Delivery Guarantees?C B F T A S

36. What about Delivery Guarantees?C B F T A B S

37. What about Delivery Guarantees?F S

38. What about Delivery Guarantees?
GPVFR forwarding loop in arbitrary graphs F T

39. Is this an Issue for Greedy + PVFR?B  S
Start here.  F T A

40. Example 4
Greedy Other Adaptive Face Routing GOAFR, [Kuhn et al., 2003]

41. Face Routing Part of GOAFRS T F
P  S
repeat
Explore the complete boundary of face F containing the line PT
Advance to Q on F’s boundary which is closest to T and set P  Q
until reaching T

42. Face Routing Part of GOAFRQ S T F
P  S
repeat
Explore the complete boundary of face F containing the line PT
Advance to Q on F’s boundary which is closest to T and set P  Q
until reaching T

43. Face Routing Part of GOAFRQ S T F
P  S
repeat
Explore the complete boundary of face F containing the line PT
Advance to Q on F’s boundary which is closest to T and set P  Q
until reaching T

44. Face Routing Part of GOAFRS T Q P
P  S
repeat
Explore the complete boundary of face F containing the line PT
Advance to Q on F’s boundary which is closest to T and set P  Q
until reaching T

45. What about the GPVFR Loop?S F T

46. Observation Difference between GPVFR and GOAFR
GOAFR: Sequence of source destination lines PiT which satisfy |Pi+1T| < |PiT|
GPVFR: Two successive source destination lines might satisfy |Pi+1T| ≥ |PiT|
However, when starting exploration of F in S, is there always a point P on F which satisfies |PT| < |ST|?

47. State of the Art
Counter examples for some well established mechanisms which are proved to be correct
Proofs do not consider the details of localized face selection
General question: Does face and combined greedy-face routing provide delivery guarantees???

48. General Face Start Mechanism
Assumption
Planar graph
S and T are connected
Mechanism
Select first edge SA in cw direction from ST; traverse by right hand rule
Or select first edge SB in ccw direction from ST; traverse by left hand rule
Invariant: Always detects an ST-intersection P≠S S A B V U P T

49. General Face Change Mechanism
Precondition
Planar Graph
S and T are connected
S and U are connected
UV intersects ST
Mechanism
If UT right of UV then traverse by left hand rule
else traverse by right hand rule
Invariant: Always detects a PT-intersection Q≠P
(a) V
left
right T S
ccw≤180°
cw<180° U
(b) V T Q S P U

50. RNG and GG are Good Natured
Face change is not an issue in GG and RNG
Intersection Property of GG
RNG  GG  applies to RNG as well U T
WLOG: |UT| < |ST| S V

51. Summary Success of face routing applied on its own RNG GG LDT Any GFGok
GPSR
loop
GOAFR
GPVFR ?

52. Summary Success of combined greedy-face routing RNG GG LDT Any GFG ok
GPSR ?
loop
GOAFR
GPVFR

53. Summary GG and RNG allow simplified scheme Repeat Until delivery
Greedy as long as possible
Traverse single face until return to greedy possible
Until delivery