Cluster construction
research in mobile ad
hoc network
NTUIM92 R92725034
資管所研二 林明源
IM Graduate Lin Ming Yuan
Outline

Problem statement

Previous work





Cluster construction
Mobility research
Integer formulation for clustering
Energy-efficient multicasting and wireless advantage
My work
Problem statement (1/2)

For specific applications like military missions, emergency response
operations, electronic community communication etc, we desire to
construct a cluster topology in mobile ad hoc network
including following considerations：

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Wireless communication advantage
Individual/Group-based mobility pattern
Cluster coordinator/manager selection (clusterhead)
Resource management and allocation in clusters
Connectivity
Stability
Reliability
Efficient routing through clusterhead
Problem statement (2/2)
Cluster member
Clusterhead
Gateway node
Intra-Cluster link
Cross-cluster link
In the remaining slides, I will describe the issues mentioned above in detail,
summary of the previous related works and methodologies and my work.
Outline

Problem statement

Previous work





Cluster construction
Mobility research
Integer formulation for clustering
Energy-efficient multicasting and wireless advantage
My work
Cluster construction(1/10)

A mobility-based clustering approach to support mobility
management and multicast routing in mobile ad-hoc
networks [international journal of network management 2001;11:387-395][Author:Beongku
An, Symeon Papavassiliou ]

MHMR: mobility-based hybrid multicast routing protocol
un mobile ad hoc wireless network [wireless communication and mobile
computing2003;3:255-270][Author:Beongku An, Symeon Papavassiliou ]

Geomulticast: architecture and protocols for mobile ad
hoc wireless networks [www.ComputerScience Web.com received 17 October
2002][Author:Beongku An, Symeon Papavassiliou ]
Cluster construction(2/10)

For some location-based reasons like regional network
management and resource allocation and scalability etc.,
we desire to partition nodes to subsets. And clustering
is the method to organizes unlabeled nodes into groups
by using feature vectors (such as similar mobility pattern).
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High cost to reconstruct the topology and election when clusterhead move out the
coverage of the cluster.
Reconstruction causes the variation of the scheduling and allocation and
downsize the performance and utilization.
Stability in location and less mobility are more important.
In MHMR, the author proposed MBC approach that use
a combination of both physical and logical partitions
of network (ex. geographic proximity and functional relation between nodes,
such as mobility pattern, etc.)
Cluster construction(3/10)

From observations of the group mobile behavior, the
author want to propose a Mobility-based Hybrid Multicast
Routing (MHMR) which has the following three features
and considerations:
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Mobility-based clustering and group-based hierarchical structure
Group-based (limited) mesh structure and forwarding tree concept
Combination of proactive and reactive concepts providing low acquisition delay
and low overhead
Channel access and code separation
Power control and bandwidth allocation
Mobility management
MHMR: mobility-based hybrid multicast routing
protocol un mobile ad hoc wireless network Cluster
construction (mobility pattern)(4/10)

Relative velocity V(m,n,t) between the node m and n is
defined as : V (m, n, t )  V (m, t )  V (n, t )

Average relative mobility M m,n,T between any pair (m,n) of
nodes during time period T is defined as: M m,n,Y  1 nNi V (m, n, t i )
N

Average motion behavior of a cluster Ci is defined as:
CM 1i 

1
M

K Ci
V (n k , T )
Average relative mobility within the cluster Ci is defined as:
CM 2 i 
1
N

( m , n )Ci
M m, m,T
MHMR: mobility-based hybrid multicast
routing protocol un mobile ad hoc wireless
network Cluster construction (heuristic)(5/10)

Step1.Mobility Information Dissemination

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Step2.Calculating Mobility Metrics


Each node n periodically disseminate its velocity information
(V(n,ti),i=1,2…) to its neighboring nodes.
Upon reception of neighboring nodes’ velocity information, each node
calculate the relative velocity V(m,n,T) of each pair nodes and exchange
periodically.
Step3.Initial Cluster Construction


Construct the set Sm includes node m and all the nodes from which
node m receives mobility information.
Among the nodes of Sm the node-i with the lowest ID that satisfies the
following condition: Mm,i,T < Thmob .Node i € Sm is selected as a
tentative clusterhead. That is
MHMR: mobility-based hybrid multicast
routing protocol un mobile ad hoc wireless
network Cluster construction (heuristic)(6/10)

Thmod is the mobility threshold parameter for the
network stability. (random node’s mobility or group
mobility)
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Step4.Clustering merging
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According to the step 3, a parent clusterhead can include the other child
clusterheads as long as satisfying the TCH criteria and under the upper
bound of the number of hops (L).
Step5.Cluster Maintenance and Reconstruction

When a node m moves into the cluster Cj and the clusterhead node n in
cluster Cj still satisfies the condition : Mm,i,T < Thmob , it’s not
necessary to reconstruct the cluster and elect new clusterhead. Then the
node m request to clustering to node n. Otherwise node m repeats step
5 during this motion, elect new clusterhead among these nodes and
reconstruct the cluster
MBC approach (reference)(7/10)
Cluster construction- other proposed
approach(8/10)

Max-min D-cluster formation in wireless ad hoc
networks [inforcom 2000] [Author:Alan D. Amis Ravi Prakash Thai, H.P.Vuong
Dung T. Huynh Department of Computer Science University of Texas at Dallas]

A multicast routing protocol for ad hoc network
[processing of inforcom99 784-792 March 99] [J.J. Garcai-Luna-Aceves and Ewerton
L. Madruga]
Max-min D-cluster formation in
wireless ad hoc networks(9/10)
The heuristic runs for 2d rounds of information
exchange. Each node maintains two arrays, WINNER
and SENDER, each of size 2d node ids: one id per
round of information exchange.
First round to select maximum ID as clsusterhead and
second round to adjust the selected CH by minimum
ID for load balance consideration.
A multicast routing protocol for
ad hoc network(10/10)
Shared core-based multicast tree for each group and construct a mesh from
different group trees.
The source node transmits the traffic to the core node and downstream multicast
to the tree members.
New members join via group tree members or trace the neighbor to the core node
(tree manager).
Outline

Problem statement

Previous work





Cluster construction
Mobility research
Integer formulation for clustering
Energy-efficient multicasting and wireless advantage
My work
Mobility research(1/8)

A survey of mobility model for ad hoc network
research [wireless communication and mobile computing 2002;2:483502][author: Tracy camp, Jeff Boleng, and Vanessa Davies]

ODMRP On-demand multicast Routing Protocol
in Multihop Wireless Mobile Networks [Mobile Network
and Application; Dec 2002;7,6;ABI/INFORM Global][Authors: Sung-Ju Lee, William
Su, Mario Gerla]
A survey of mobility model for ad
hoc network research(2/8)
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Two type of the mobility models
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Independent (entity mobility model)- Entity mobility models : mobility models that
represent mobile nodes whose movements are independent of each other.
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Random walk mobility model (the most common)
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Random waypoint mobility model (the most common)
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Random direction mobility model
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A boundless simulation mobility model
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Gauss-Markov mobility model
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A probabilistic mobility model
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City section mobility model
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Dependent (group-based mobility model)- In an ad hoc network, however, there are
many situations where it is necessary to model the behavior of MNs as they move together.
So the movement of MNs may depend on other’s (reference point) behavior.
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Exponential correlated random mobility model
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Column mobility model
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Nomadic community mobility model
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Pursue mobility model
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Reference point group mobility model
Random walk mobility model(3/8)

The random walk mobility model was first described mathematically by Einstein
in 1926 in order to mimic erratic motion such as Brown Motion.

In this mobility model, a MN moves from its current location to a new location by
randomly choosing a direction and speed in which to travel at a predefined step
number or time slots. After choosing a new speed and direction, the new path is
decided.
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The new speed and direction are both chosen from [speedmin, speedmax] and
[0, 2π]
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The model is a memoryless mobility pattern because it retains no knowledge
concerning its past locations and speed values when deciding the next speed
and direction. (The defectives can be modified by the Guass-Markov model.)

If the specified time (or specified time) a MN moves in the model is short, then
the movement pattern is a random roaming pattern restricted to a small portion
of the simulation area.
Random walk mobility model(4/8)
Start point: (150, 300)
Speed range: o~10 m/s-1
Direction:0~2π
Time slot: 60s
Gauss-Markov mobility model(5/8)

The Gauss-Markov Mobility Model was designed to adapt to
different levels of randomness via one tuning parameter. At fixed
intervals of time, n, movement occurs by updating the speed and
direction of each MN. Specifically, the value of speed and direction
at the n-th instance is calculated based upon the value of speed and
direction at the (n-1)-st instance and a random variable using the
following equations.
select n-1th Gauss r.v.: S
x
n-1th instance: Sn1 and d n-1
n-1
and d x n-1
n-th instance: Sn1 and d n-1
Gauss-Markov mobility model(6/8)
Start point: (150, 300)
Change direction mean
d
Simulation time: 1000s
α=0.75
Speed is fixed at 10 m/s-1
Mean direction is initial 90 degrees.
Eliminate the sudden stops and sharp turns. The Markov
process can be applied to the x and y equation directly instead
of through speed and direction variables.
ODMRP on-demand multicast t Routing Protocol
in Multi-hop Wireless Mobile Networks(7/8)

Adapting the Refresh Interval via Mobility Prediction
Suppose 2 nodes i and j are within the transmission range r of
each other.
(xi, yi) : co-ordinates of mobile host I
 (xj, yj): co-ordinates of mobile host j

vi and vj: speeds of i and j respectively

oi and oj: moving directions of I and j respectively
Amount of time i and j will stay connected is predicted by:


(ab  cd )  (a 2  c 2 )r 2  (ad  bc) 2
Dt 
a2  c2
(at  b)  (ct  d )  r
2

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2
a= vi cos oi - vj cos oj vj
b= xi – xj
c= vi sin oi - vi sin oj and V
d= yi - yi
i
i
θi
Vj
 at  b    ct  d 
2
θj
j
r
b
d
2
 r2
ODMRP on-demand multicast t Routing Protocol in
Multi-hop Wireless Mobile Networks-prediction(8/8)

Due to the mobility effect, it’s necessary to predict the mobility
information at t0+t1+t2+t3 first to make the decision more suitable for
the scenario at t0+t1+t2+t3. Then we use the predicted mean value
and ODMRP formula to compute the link duration (or reliability of
the consecutive path).
t0
t0+t1
t0+t1+t2
t0+t1+t2+t3
t0+t1+t2+t3+T
t1蒐集位置資訊與mobility資訊，包括速度與方向
t2 optimal algorithm computation time
t3 routing decision distribution time
T是此次決策使用的時間
在T快結束之前，保留的時段t1+t2+t3作下一次cluster的決策
Outline

Problem statement

Previous work





Mobility research
Cluster construction
Integer formulation for clustering
Energy-efficient multicasting and wireless advantage
My work
Integer formulation for clustering(1/7)

Minimum power broadcast trees for wirelessnetworks: Integer
programming formulations [INFOCOM 2003, 30 March-3 April 2003, p1001- 1010
vol.2][auhtor: Das, A.K. Marks, R.J. El-Sharkawi, M. Arabshahi, P. Gray, A. Dept. of Electr.
Eng., Washington Univ., Seattle, WA, USA]

Clique and clustering: A combinatorial approach [Mathematical Programming,
62, 133-151][author: E. L. JOHNSON, A. MEHROTRA, and G. L. NEMHAUSER, 1993. Min-cut
clustering ]

Load-balance clusters in wireless ad hoc networks [Proceedings of the 3rd
IEEE Symposium on Application-Specific Systems and Software Engineering Technology 2000,
P.25][author: alan D. Amis, Ravi Prakash]

On the optimal clustering in mobile ad hoc networks [Proceedings of IEEE
Consumer Communications and Networking, Las Vegas, Nevada USA/ January 5-8, 2004 ][author:
Jamal N. Al-Karaki Ahmed E. Kamal Raza Ul-Mustafa Laboratory for Advanced Networks Dept. of
Electrical and Computer Engineering]
Clique and clustering: A combinatorial
approach- basic model for clustering(2/7)
Min
w y
eE
e
e
(E: the link set, we: the link weight; ye: the link decision variable for
cluster) (objective to minimize the total weights of clusters)
Subject to:
K
(K: no. of clusters, zie: the belongness decision variable for node i
z 1 iV

and cluster k; V: the node set)
k 1
k
i

iV
fi zik  F
k=1,......K (F: maximum cluster capacity; maximum flow constraint for
 zik   z kj  yii
kK1
kK1
the cluster k)
K1 {1,......K},(i,j)  E
(the flow balance constraint for the multicast
tree of the cluster k)
yii ,zik  {0,1} i  V, k=1,......K Integer constraint
On the optimal clustering in
mobile ad hoc networks(3/7)

A Mobile Ad hoc Network (MANET) can be represented by a set of
logical clusters with clusterheads (CHs) acting like virtual basestations, hence forming a wireless virtual backbone. The role of
clusterhead is a temporary role, which changes dynamically as the
topology or other factors affecting it change. The proposes includes:
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Trade-off of the network performance due to the large No. of CHs
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Reduce protocol overhead
Minimize storage requirement
Hop count
Communication overhead
Extra energy consumption
In this paper, the author proposed a heuristic approach VGA (virtual
grid architecture) and ILP formulation for clustering.
On the optimal clustering in mobile
ad hoc networks-heuristic(4/7)
In VGA clustering, the
network area is divided into
fixed, disjoint, and regular
shape zones (square). Each
mobile node is a member of
one of those zones and its
zone membership is
determined based on its
location in the network area.
The clusterheads of adjacent
zones can communication to
each other directly. If the
zone has only short range
nodes, the zone is further
divided into four sub-zones.
On the optimal clustering in mobile
ad hoc networks- heuristic(5/7)
The extension to diagonal
routing, henceforth called
Diagonal VGA (D-VGA), is
possible but it may complicate
routing since the number of
potential neighbor zones
doubles.
In D-VGA CHs can
communication with CHs of
diagonal zones besides the
vertical and horizontal zones.
On the optimal clustering in mobile
ad hoc networks- formulation(6/7)
ILP notation
On the optimal clustering in mobile
ad hoc networks- formulation(7/7)
Formulation
The belonging constraint
The link usage constraint
The xii constraint
The existence of inter-cluster routing
The inter-cluster routing constraint use CH as
intermediate nodes
Outline

Problem statement

Previous work





Mobility research
Cluster construction
Integer formulation for clustering
Energy-efficient multicasting and wireless advantage
My work
Energy-efficient multicasting and wireless
advantage(1/6)

Algorithms for energy-efficient multicasting in
static ad hoc network [Mobile Networks and Applications 6,251263,2001][Author： JEFFREY E. , WIESELTHIER, GAM D. NGUYEN Information
Technology Division, Naval Research Laboratory, Washington]

On reducing broadcasting redundancy in ad hoc
network [IEEE transactions on mobile computing April-June 2002][Author: Wei
Lou, Student Member, IEEE, and Jie Wu, Senior Member]
Algorithms for energy-efficient multicasting in static ad
hoc network - Wireless communication advantage (2/6)

Normalize transmission power on link (I,j) by range r and
proportional factor Pij = power needed to support link
between nodes i and j =rα where r is the distance between
nodes i and j and α is the decade factor
Pi,(j,k) = max{Pij, Pik } is sufficient
to reach both node j and node k,
based on our assumption of
omnidirectional antennas.“Wireless
Multicast advantage”
Cited from [Algorithms for EnergyEfficient Multicasting in Static Ad Hoc
Wireless Networks] Mobile Networks
and Applications 6,251-263,2001
Algorithms for energy-efficient multicasting in static ad
hoc network - suggested approach (3/6)

By the way, transmission power range affect
connectivity and construction of spanning tree. Some
additional nodes may be needed as relay to provided
connectivity to all memberships of the multicast
group. (relayed nodes)

Two basic approaches to construct multicast tree and
using PIM (Spare mode of the protocol independent
Multicasting) on the trees
- Source-Based Tree (SBT)
- Core-Based Tree (CBT)
On reducing broadcasting redundancy in ad hoc
network (DP) – energy-efficient consideration (4/6)

For reducing redundancy transmissions and
prolong the life of the network, the DP algorithm
utilizes 2-hops neighborhood information.
Node v uses N(N(u)), N(u), and N(v)
to obtain U(u, v) = N(N(v)) - N(u) N(v) and B(u, v) = N(v) - N(u).
Node v then calls the selection
process to determine F(u, v)
(forward node list).
Cited from [On Reducing Broadcast
Redundancy in Wireless Ad Hoc Network]
Wei Lou, Student Member, IEEE, and Jie
Wu, Senior Member, IEEE From IEEE
transactions on mobile computing AprilJune 2002
On reducing broadcasting redundancy in ad hoc
network (TDP) – energy-efficient consideration (5/6)
If node v can receive a packet
piggybacked with N(N(u)) from
node u, the 2-hop neighbor set
that needs to be covered by v’s
forward node list F is reduced to
U = N(N(v)) – N(N(u)).
Node v uses N(N(u)), N(u), and
N(v) to obtain U(u, v) = N(N(v)) –
N(N(u)) and B(u, v) = N(v) N(u).
On reducing broadcasting redundancy in ad hoc
network (PDP) – energy-efficient consideration (6/6)
Besides excluding N(u) and N(v)
from N(N(v)), as addressed in
the DP algorithm, more nodes
can be excluded from N(N(v)).
These nodes are the neighbors
of each node in N (u)  N (v) . Such
a node set is donated as.
P(u, v)  N ( N (v)  N (u ))
Node v uses N(N(u)), N(u), and
N(v) to obtain and P(u, v)  N ( N (v)  N (u ))
U = N(N(u)) - N(u) - N(v) – P, B =
N(v) – N(u).
Outline

Problem statement

Previous work





Mobility research
Cluster construction
Integer formulation for clustering
Energy-efficient multicasting and wireless advantage
My work
My work- problem statement

Assumption (given parameter and environment situation)






Node set and link set
All possible paths between any node pair (pre-computed)
O-D pair and desired traffic load
Capacity for each node
Mobility information of each node (location, velocity and direction)
For location-based management and resource allocation in dynamic
MANETs, I want to group the nodes into cluster including the
following considerations:






Determine the relationship for clusterhead and cluster member for each node pair
Determine which node would be selected as a CH
Determine the inter-cluster routing between the clusterhead and cluster members
Determine the gateway node between two clusters
Determine the link used for the cluster construction
Determine the O-D pair routing path
My worknotation
Given parameters
Notation
Definition
V
The set of nodes which is also the candidate clusterhead nodes
set
L
The set of links
d
The max hop count to construct a cluster which is the longest
distance between a cluster member and the selected
clusterhead
Puv
Candidate path set from node u to the node v
W
The set of all O-D pairs
Pod
The set of candidate paths for O-D pair (o,d) which will be
included by Puv, Pod  Puv
Cn
Capacity for the node n which is evaluated by residual battery
power seconds
aw
Traffic demand for the O-D pair which is evaluated by
transmission time seconds
Hw
Maximum allowed hop count for the O-D pair w
pl
1 if the link l is on the path p, and 0 otherwise
pn
1 if the node n is on the path p, and 0 otherwise
xn(t)
The x-axis coordinate of the node n at time t
yn(t)
The y-axis coordinate of the node n at time t
Vx(t)
The x-axis velocity of the node n at time t
Vy(t)
The y-axis velocity of the node n at time t
tij
The link duration between node i and node j
My work- notation
Decision variables
Notation
Definition
hg
1 if node g is selected to be a clusterhead. 0 otherwise.
bvg
1 if node v belongs to cluster g. 0 otherwise
xpvg
The node v choices the path p connect to the clusterhead g.
γvmn
1 if node v is belong to the cluster m and is selected as the
gateway to the cluster n.
ygl
1 if clusterhead g selects the link l for the cluster g construction
ηqod
1 if path q  Pod is used to transmit the packet for the O-D pair
w. Otherwise, 0.
My work- formulation
Objective function:
maxT  W
Maximize the minimum link T
duration and node duration W
Subject to:
b
gV
1
vg
v V
bvg  hg
v, g V
x
v, g V
pPvg
pvg
 bvg
(1)
The cluster member belonging
constraint
(2)
(3)
The intra-cluster routing
constraint
x
pvg
p  d
p  Pvg v, g  V
y
g
  bvg  1
g  V
L
L
x
pPvg
vV
pvg
 pl  yg
v, g V
The d-hop routing
(4)
constraint
(5)
L
The intra-cluster routing constraint for subtree-construction
(6)
My work- formulation
CH
Cluster member
Clusterhead
v
Constraint (3):
Node v 到CH間存在多條paths
Constraint (5) (6):
Node v 到CH間存在多條paths
My work- formulation
uv
(bvm  bun )   vmn   unm
 vmn   unm 
uv
u , v, m, n  V
(2bvm  2bun  2)
u , v, m, n  V
(7) gateway node constraint
The cluster
(8)
 vmn  bvm
node belonging constraint
v, m  V The cluster gateway
(9)
r
m V
vV
vmn
1
The (10)
cluster connectivity constraint
g V ,  L
T  yg  t
T  t1  t2  t3
t0
(11)cluster duration constraint
The
(12)
t0+t1
t0+t1+t2
t0+t1+t2+t3
T
t0+t1+t2+t3+T
My work- formulation
Cluster n and CH n
uv
Cluster m and CH m
Gateway node v, u between cluster m and n
Constraint (7) (8):The cluster gateway node constraint
若u、v兩個nodes相鄰(存在有hop count為一的路徑)，且u、
v兩個nodes分屬不同的cluster m和n。則u、v為兩cluster的
gateway node。
bum
bvn
 umn
 vnm
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
1
1
1
1
My work- formulation
x
pPw
x
nV
p
p
pPw
w W
  pn  H w
x
p
1
pl
The O-D pair routing
(13) constraint
p  Pw , w W
 yg
w W
(14)
L
(15)
The inter-cluster routing constraint
qod   qn  x png   pm   qm
Ln 
a  x
wW
w
pPw
Wn  Cn  Ln
p
  pn  Cn
(o, d )  W p  Png n,m  V
n V
n V
(16)
The node capacity
(17)constraint
(18)
My work- formulation
hg  0 or 1
g  V
(19)
bvg  0 or 1
v, g V
(20)
x pvg  0 or 1
p  Puv ; u, v V
(21)
The integer constraint x 6
 vmn  0 or 1
v, m, n V
(22)
y g  0 or 1
g V ;  L
(23)
x p  0 or 1
p  Pw
(24)
End
 Thanks
for your attention
 Discussion