![](bg9.png)
Input: A tuple (i, u, v, D, modeGreedy, modeFace),
s = node that initiate the current face routing, u =
past node, v = current node, D = destination node,
the mode indicators are boolean.
Initialization: u = nil, v = current node,
modeGreedy= true, modeFace= false.
Output: Select the next node w and set the mode
indicators modeGreedy, modeFace.
if N
v
=
/
0 then return error // disconnected node
if modeGreedy then select w ∈ s
v
D
∩ s
D
v
∩ N
v
//
selection mechanism is free
if w 6= nil then return
(i, v, w, D, modeGreedy, modeFace)
else modeFace = true
if modeFace then
if modeGreedy then // here we start Face
routing
modeGreedy=false
select w ∈ N
v
for x ∈ N
v
do
w =nextto(v, D, w, x)
return (v, v, w, D, modeGreedy, modeFace)
else // here we continue face routing
if s
i
D
∩ s
D
i
∩ N
v
6=
/
0 then // we switch to
Greedy routing
select any node w in the intersection
modeGreedy = true, modeFace = false
return
(nil, nil,w,D, modeGreedy, modeFace)
else
if w ∈ N
v
and | N
v
|= 1 then return
(i, v, w, D, modeGreedy, modeFace)
else select w ∈ N
v
for x ∈ N
v
\ {w}
w =FaceNextEdge(v, u, w, x)
if v → w
satisfy one of the conditions (2) then //switch the
face
return
(i, w, v, D, modeGreedy, modeFace) // v routes data
else
return
(i, v, w, D, modeGreedy, modeFace)// continues
Figure 11: Implementation of the routine
FaceNextEdge(u,v,w,z).
posed to be promising mainly due to its simplicity
offered in wireless sensor network environments.
Even though, partial nature of geographic information
carried by VRAC coordinates make geographic
routing not so trivial. Especially in the absence
of fundamental geometric concepts like angle and
distance, raw coordinate systems require a different
approach to perform geographic routing algorithms.
0
2
4
6
8
10
2 3 4 5 6 7 8 9
Stretch Factor
Average Node Degree
Stretch Factor
GFG + Gabrial
VRAC Routing + Schnyder
Figure 12: Stretch factor vs node density for VRAC and
Euclidean coordinate systems.
In this paper we take a combinatorial approach to
construct basic properties needed to perform both
greedy and face routing phases. Further more we
prove that, based on those constructs it can perform
delivery guaranteed face routing in arbitrary graphs.
We evaluate our approach with standard geographic
routing algorithm GPSR comparing the stretch factor.
As the first attempt in this line of research towards
geographic face routing, we further believe that the
combinatorial constructs could demonstrate resilience
towards erroneous distance measures. Further more
we believe that, with future contributions our approach
would be a candidate with real wireless sensor network
characteristics.
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CombinatorialApproachforGeographicRoutingwithDeliveryGuarantees
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