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

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

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

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]

GPSR – The FACE Routing Part x 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]

GPSR – The FACE Routing Part x 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]

GPSR – The FACE Routing Part x 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]

GPSR – The FACE Routing Part x 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]

GPSR – The FACE Routing Part x “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]

What about Delivery Guarantees? C E

What about Delivery Guarantees? C E Outer Face

What about Delivery Guarantees? C E Outer Face

What about Delivery Guarantees? C E

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

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

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

GFG – The face routing part 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

GFG – The face routing part Q 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

GFG – The face routing part 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

GFG – The face routing part 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

What about the GPSR Loop? D C E Outer Face

What about the GPSR Loop? D C E Outer Face

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

What about the GPSR Loop? D C E Outer Face

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?

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

GPVFR – The Face Routing Part 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]

GPVFR – The Face Routing Part 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]

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]

GPVFR – The Face Routing Part S 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]

GPVFR – The Face Routing Part S 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]

What about Delivery Guarantees?

What about Delivery Guarantees? F T B

What about Delivery Guarantees? C

What about Delivery Guarantees? C B F T A S

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

What about Delivery Guarantees? F S

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

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

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

Face Routing Part of GOAFR 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

Face Routing Part of GOAFR Q 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

Face Routing Part of GOAFR Q 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

Face Routing Part of GOAFR S 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

What about the GPVFR Loop? S F T

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|?

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???

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

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

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

Summary Success of face routing applied on its own RNG GG LDT Any GFG ok GPSR loop GOAFR GPVFR ?

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

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