On Delivery Guarantees of Face and Combined Greedy-Face Routing in Ad Hoc and Sensor Networks
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Transcript of On Delivery Guarantees of Face and Combined Greedy-Face Routing in Ad Hoc and Sensor Networks
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On Delivery Guarantees of Face and Combined Greedy-Face Routing in Ad Hoc and Sensor Networks
Hannes Frey, Ivan Stojmenovic
MobiCom 2006
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Face Recovery Details
When to change current face traversal?
How to decide the next face locally?
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Example 1Greedy Perimeter Stateless Routing
GPSR [Karp, Kung, 2000]
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GPSR – The FACE Routing Part
TS
“ 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]
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GPSR – The FACE Routing Part
TS
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]
x
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GPSR – The FACE Routing Part
F1 F2TS
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]
x
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GPSR – The FACE Routing Part
TS
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]
x
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GPSR – The FACE Routing Part
S
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]
x
T
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GPSR – The FACE Routing Part
TS
“ 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]
x
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What about Delivery Guarantees?
A
B
C
D
E
S T
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What about Delivery Guarantees?
A
B
C
D
E
S T
Outer Face
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What about Delivery Guarantees?
A
B
C
D
E
S T
Outer Face
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What about Delivery Guarantees?
A
B
C
D
E
S T
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What about Delivery Guarantees?
A
B
C
D
E
S T
GPSR Forwarding Loop for GG, RNG, and LDT
x
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Is this an Issue for Greedy + PSR?
S
A
B
C
D
E
T
F1
F2
P
Q
[Kim et al., 2005]
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Example 2Greedy-Face-Greedy GFG, [Bose et al.,
1999]
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GFG – The face routing part
P Srepeat
Let F be the face with P on boundary and intersecting PTTraverse* F until reaching an edge that intersects PT at some point Q≠PP Q
until P=T
*counterclockwise if inner, clockwise if outer face
TS
P
F
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GFG – The face routing part
P Srepeat
Let F be the face with P on boundary and intersecting PTTraverse* F until reaching an edge that intersects PT at some point Q≠PP Q
until P=T
*counterclockwise if inner, clockwise if outer face
TS
Q
F
P
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GFG – The face routing part
P Srepeat
Let F be the face with P on boundary and intersecting PTTraverse* F until reaching an edge that intersects PT at some point Q≠PP Q
until P=T
*counterclockwise if inner, clockwise if outer face
TS
F
P
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GFG – The face routing part
P Srepeat
Let F be the face with P on boundary and intersecting PTTraverse* F until reaching an edge that intersects PT at some point Q≠PP Q
until P=T
*counterclockwise if inner, clockwise if outer face
TS
P
F
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What about the GPSR Loop?
A
B
C
D
E
S T
Outer Face
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What about the GPSR Loop?
A
B
C
D
E
S T
Outer Face
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What about the GPSR Loop?
A
B
C
D
E
S T
Outer Face
Select face with P on boundary and intersecting PT
P
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What about the GPSR Loop?
A
B
C
D
E
S T
Outer Face
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Example 3Greedy Path Vector Face Routing
(GPVFR) [Leong, Mitra, Liskov, 2005]
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GPVFR – The Face Routing Part
S T
A
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]
F
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GPVFR – The Face Routing Part
S T
A
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]
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GPVFR – The Face Routing Part
S T
A
B
C
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]
S := C
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GPVFR – The Face Routing Part
S T
S
B
A
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]
F
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GPVFR – The Face Routing Part
S T
S
B
A
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]
F
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What about Delivery Guarantees?
S
T
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What about Delivery Guarantees?
S
A
T
B
F
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What about Delivery Guarantees?
S
A
C
T
B
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What about Delivery Guarantees?
CB
S
T
A
F
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What about Delivery Guarantees?
CB
T
B
A
S
F
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What about Delivery Guarantees?
T
S
F
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What about Delivery Guarantees?
S
TF
GPVFR forwarding loop in arbitrary graphs
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Is this an Issue for Greedy + PVFR?
B
S
A
TF
Start here.
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Example 4 Greedy Other Adaptive Face Routing
GOAFR, [Kuhn et al., 2003]
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Face Routing Part of GOAFR
P Srepeat
Explore the complete boundary of face F containing the line PTAdvance to Q on F’s boundary which is closest to T and set P Q
until reaching T
S T
F
P
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Face Routing Part of GOAFR
P Srepeat
Explore the complete boundary of face F containing the line PTAdvance to Q on F’s boundary which is closest to T and set P Q
until reaching T
S T
Q
F
P
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Face Routing Part of GOAFR
P Srepeat
Explore the complete boundary of face F containing the line PTAdvance to Q on F’s boundary which is closest to T and set P Q
until reaching T
S T
Q
F
P
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Face Routing Part of GOAFR
P Srepeat
Explore the complete boundary of face F containing the line PTAdvance to Q on F’s boundary which is closest to T and set P Q
until reaching T
S T
Q
F
P
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What about the GPVFR Loop?S
TF
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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???
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General Face Start Mechanism
Assumption Planar graph S and T are connected
MechanismSelect 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
T
S
A B
U VP
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General Face Change Mechanism
Precondition Planar Graph S and T are connected S and U are connected UV intersects ST
MechanismIf UT right of UV then traverse by left hand rule
else traverse by right hand rule
Invariant: Always detects a PT-intersection Q≠P
T
U
V
rightleftS
cw<180°
ccw≤180°
TS
U
(a)
V
P Q
(b)
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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
T
S
U
V
WLOG: |UT| < |ST|
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Summary Success of face routing applied on its
ownRNG GG LDT Any
GFG ok ok ok okGPSR loop loop loop loopGOAFR ok ok ok okGPVFR ? ? ? loop
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Summary Success of combined greedy-face
routingRNG GG LDT Any
GFG ok ok ok okGPSR ok ok ? loopGOAFR ok ok ok okGPVFR ok ok ? loop
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Summary GG and RNG allow simplified scheme
RepeatGreedy as long as possibleTraverse single face until return to greedy possible
Until delivery