Chapter 5 Topology Control

1
Chapter 5Topology Control
2
Outline

• 5.1. Motivations and Goals
• 5.2. Power Control and Energy Conservation
• 5.3. Tree Topology
• 5.4. k-hop Connected Dominating Set
• 5.5. Adaptive node activity
• 5.6. Conclusions

3
Outline

• 5.1. Motivations and Goals
• 5.2. Power Control and Energy Conservation
• 5.3. Tree Topology
• 5.4. k-hop Connected Dominating Set
• 5.5. Adaptive node activity
• 5.6. Conclusions

4
Motivations

• A typical characteristic of wireless sensor
  networks
• deploying many nodes in a small area
• ensure sufficient coverage of an area, or
• protect against node failures
• Networks can be too dense too many nodes in
  close (radio) vicinity

5
Motivations

• In a very dense networks, too many nodes
• Too many collisions
• Too complex operation for a MAC protocol
• Too many paths to be chosen from for a routing
  protocol,

6
Goals

• This chapter looks at methods to deal with such
  networks by
• Reducing/controlling transmission power
• Deciding which links to use
• Turning some nodes off

7
Topology Control

• Topology control Make topology less complex
• Topology
• Which node is able/allowed to communicate with
  which other nodes
• Topology control needs to maintain invariants,
  e.g., connectivity

8
Options for topology control
9
Outline

• 5.1. Motivation and Goals
• 5.2. Power Control and Energy Conservation
• 5.3. Tree Topology
• 5.4. k-hop Connected Dominating Set
• 5.5. Adaptive node activity
• 5.6. Conclusions

10
Introduction of Power Control

• Power control
• The transmitters power can be adjusted
  dynamically over a wide range
• Typical radio adjusts their transmitters power
  based on received signal strength

11
Introduction of Power Control

• Interactions

Power control
Large Battery makes Longer Lifetime
Battery drain
12
Introduction of Power Control

• Interactions

C
Interference
Large Power makes Performance Degradation
Source
D
Destination
Power control
Large Battery makes Longer Lifetime
Battery drain
13
Introduction of Power Control

• Interactions

Interference
C
Large Power makes Performance Degradation
Source
D
Destination
Power control
Different Power makes Load Unbalancing
Large Battery makes Longer Lifetime
D
Destination
C
B
Adjusting power can balance the power consumption
A
Source
A consumes much more power than C
Battery drain
14
Introduction of Power Control

• Interactions

C is forbid to communication with B
Adjusting the power of A can improve the spatial
reuse
B
C
D
Interference
A
C
E
Large Power makes Performance Degradation
Small Power creates more Spatial Reuse
Opportunities
Source
D
Destination
Power control
Different Power makes Load Unbalancing
Large Battery makes Longer Lifetime
D
Destination
B
Source
A consumes much more power than C
Battery drain
15
Introduction of Power Control

• Interactions

Adjusting the power of A can improve the spatial
reuse
B
C
D
Interference
A
C
E
Large Power makes Performance Degradation
Small Power creates more Spatial Reuse
Opportunities
Source
D
Destination
Power control
Different Power makes Load Unbalancing
Small Power causes More Retransmissions
Large Battery makes Longer Lifetime
Error rate
D
Destination
B
Large power, small error rate
Source
A consumes much more power than C
Battery drain
dB
16
Introduction of Power Control

• Targets and Issues
• Improve network throughput
• Improve transmission range
• Improve fairness
• Improve connectivity
• Power control helps in scheduling
• Reduce the interference and energy consumption
• Partial combination of above targets
• etc.

17
Power Control and Energy Conservation
Topology Control of Multihop Wireless Networks
using Transmit Power Adjustment
R. Ramanathan and R. Rosales-Hain
IEEE INFOCOM 2000
18
Introduction

• Topology
• The set of communication links between node pairs
  used by routing mechanism
• Uncontrollable factor mobility, weather,
  interference, noise
• Controllable factor transmission power, antenna
  direction

19
Introduction

• A graph is called connected if every pair of
  distinct vertices in the graph can be connected
  through some path
• A bi-connected graph is a connected graph that is
  not broken into disconnected pieces by deleting
  any single vertex (and its incident edges)

20
Motivation

• Drawbacks of wrong topology
• Reduce network capacity
• Increase interference
• Increase end-to-end packet delay
• Sparse network
• A danger of network partitioning
• High end to end delays
• Dense network
• Many nodes interfere with each other

21
Static Networks Min-Max Power Algorithm

• Goal
• Find a per-node minimal assignment of transmitted
  power p
• such that (1) the induced graph is connected
  and (2) max p is minimum

22
Min-Max Power Algorithm- Connected Networks

• Phase I CONNECTION
• Construct a Minimum cost spanning tree

Successful transmit power between i and j
4
s the receiver sensitivity
23
Min-Max Power Algorithm- Connected Networks

• Phase II Per Node Minimizing Power

4
A has a path to B via C with smaller power ?A
adjusts the transmitted power from 2 to 1.
B has a path to A via D with smaller power ?B
adjusts the transmitted power from 2 to 1.
The edge (A, B) can be disconnected to save more
energy
24
Min-Max Power Algorithm- Bi-Connectivity
Augmentation

• Phase I BICONN-AUGMENT
• Construct a Connected Minimum cost spanning tree

Successful transmit power between i and j
4
s the receiver sensitivity
25
Min-Max Power Algorithm- Bi-Connectivity
Augmentation

• Phase I BICONN-AUGMENT
• Add (u, v) to graph G until the network is
  bi-connected

Bi-Connected component of C
Bi-Connected component of D
Bi-Conn. Comp. of C ? Bi-Conn. Comp. of D
gt Add (C, D)
26
Min-Max Power Algorithm- Bi-Connectivity
Augmentation

• Phase I BICONN-AUGMENT
• Add (u, v) to graph G until the network is
  bi-connected

Bi-Connected component of E
Bi-Connected component of F
Bi-Conn. Comp. of E ? Bi-Conn. Comp. of F
gt Add (E, F)
27
Min-Max Power Algorithm- Bi-Connectivity
Augmentation

• Phase II Per Node Minimizing Power
• No side-effect-edge ?Finish

28
Min-Max Power Algorithm- Bi-Connectivity
Augmentation

• Phase II Per Node Minimizing Power
• An other example has side-effect-edge

1
B
A
3
3
3
2
D
C
2
Disconnect the edge (A, C) and still
Bi-Connectivity ?C adjusts the transmitted power
from 3 to 2
29
Min-Max Power Algorithm- Bi-Connectivity
Augmentation

• Phase II Per Node Minimizing Power
• An other example has side-effect-edge

Disconnect the edge (B, D) and still
Bi-Connectivity ?B adjusts the transmitted power
from 3 to 2
1
A
B
2
3
3
3
D
2
C
30
Min-Max Power Algorithm- Bi-Connectivity
Augmentation

• Phase II Per Node Minimizing Power
• Finish

31
Outline

• 5.1. Motivation and Goals
• 5.2. Power Control and Energy Conservation
• 5.3. Tree Topology
• 5.4. k-hop Connected Dominating Set
• 5.5. Adaptive node activity
• 5.6. Conclusions

32
Introduction of Tree Topology Control

• Example
• MPR (Multi-Point Relay) election

(a)
(b) is better than (a)
33
Introduction of Tree Topology Control

• Example

(a)
(b)
a to d needs 2 hops
a to d needs 7 hops
(a) is better than (b)
34
Tree Topology
Design and Analysis of an MST-Based Topology
Control Algorithm
N. Li, J. C. Hou, and L. Sha
IEEE INFOCOM 2003
35
Motivation

• The advantage of Topology Control
• Minimize the overhearing and then optimize the
  network spatial reuse
• Maintain a connected topology by minimal power
• Power-efficient

(1) No Topology Control
36
Goal

• Determine the transmission power of each node
• Maintain network connectivity
• Minimal power consumption

37
Local Minimum Spanning Tree Algorithm (LMST)

• Local Minimum Spanning Tree Algorithm (LMST)
• Step 1 Information Collection
• Step2 Topology Construction
• Step3 Determination of Transmission Power

38
LMST Step1 Information Collection

• Information Exchange
• Each node broadcasts periodically a Hello message
  using its maximal transmission power.
• The Hello message includes the ID and Location of
  the node.

39
LMST Step1 Information Collection

• Information Exchange
• Since Hello message includes the nodes ID and
  Location, after obtaining the Hello message of
  1-hop neighbors, node u can construct the local
  view.

40
LMST Step2 Topology Construction

• The weight of edge between the two nodes is based
  on Euclidean distance.
• The weight of an edge also denotes the
  transmission power (or distance) between the two
  nodes

41
LMST Step 2 Topology Construction

• Each node applies Prims algorithm independently
  to obtain its Local Minimum Spanning Tree.

Node u constructs the Local Minimum Spanning Tree
using Prims algorithm according to its local view
local view of node u
According to the constructed Local Minimum
Spanning Tree, node u will use small power to
communicate with node a via node b instead of
using large power to communicate with node a
directly.
7
e
a
5
6
7
b
10
5
7
u
6

• Small power
• Creates more spatial reuse opportunity
• Decreases energy consumption

3
c
4
d
42
LMST Step 3 Determination of Transmission Power

• By measuring the receiving power of Hello
  message, each node can determine the specific
  power levels it needs to reach each of its
  neighbors.
• Two commonly-used propagation models
• Free Space
• Two-Ray

Sign Meaning
Pt Transmit power
Pr Receive power
Gt Antenna gain of the transmitter
Gr Antenna gain of the receiver
? Wave length
d Distance between nodes
L System loss
ht Antenna height of the transmitter
hr Antenna height of the receiver
43
LMST Step 3 Determination of Transmission Power

• In general, the relation between Pr and Pt is of
  the following form
• Where G is a function of
• Example
• Pth is the required power threshold to
  successfully receive the message
• Pmax is the maximal transmission power

e
Node b will compute
a
b
Hello
Data
Node b transmits data to u
Data with Pth?G
u
c
d
Hello with Pmax
44
Conclusions

• Advantages
• Maintain network connectivity by low energy
  consumption
• Reduce the probability of interference
• Increase the spatial reuse
• Achieve high throughput

45
Tree Topology
On the Construction of Energy-Efficient Broadcast
and Multicast Trees in Wireless Networks
J. Wieselthier, G. Nguyen, and A. Ephremides
IEEE INFOCOM 2000
46
Introduction

• The paper studies the problems of broadcasting
  and multicasting in wireless networks.
• To form a minimum-energy tree
• Energy efficiency
• Maintain network connectivity

47
Network Assumptions

• The power level of a transmission can be chosen
  within a given range of values.
• The availability of a large number of bandwidth
  resources.
• Sufficient transceiver resources are available at
  each of the nodes in the network.

48
Wireless Communications Model

• Node-based transmission cost evaluation
• Pi,(j,k) maxPij, Pik,
• Pij Transmission power for node i to transmit
  packets to node j

The larger power (Pik ) can cover both of node j
and node k
Pik gt Pij
j
Pij
The smaller power (Pij ) can only cover node j
i
Pik
k
49
The Broadcast Incremental Power Algorithm
5

• Assume node a is the source node
• Step 1 Determining the node that the Source can
  reach with minimum expenditure of power.

g
f
4
1.3
1.5
1.2
1.7
3
a
b
h
d
0.3
0.9
c
1
0.5
2
1.3
0.8
0.7
1.1
j
i
e
0.3
b
1
a
0.5
a
c
0
0
1
2
3
4
5
50
The Broadcast Incremental Power Algorithm

• Step 2 Determine which new node can be added
  to the tree at minimum additional cost.

5
g
f
4
?Pa
1.3
1.5
1.2
1.7
3
a
b
h
d
0.3
?Pa 0.5 0.3 0.2
0.9
c
1
1
0.5
Minimum additional cost
2
1.3
0.8
0.7
1.1
?Pb
j
i
e
1
?Pb 1 0 1
0
0
1
2
3
4
5
51
The Broadcast Incremental Power Algorithm

• Step 2 Determine which new node can be added
  to the tree at minimum additional cost.

5
g
f
?Pa
4
1.3
1.5
1.2
1.7
3
?Pa 1.3 0.5 0.8
a
b
h
d
0.3
0.9
?Pc
c
1
0.5
2
1.3
0.8
Minimum additional cost
0.7
1.1
j
i
e
?Pc 0.7 0 0.7
1
?Pb
0
0
1
2
3
4
5
?Pb 1 0 1
52
The Broadcast Incremental Power Algorithm
5

• Step 2 Determine which new node can be added
  to the tree at minimum additional cost.

g
f
4
1.3
1.5
1.2
1.7
And so forth c ? i c ? h b ? d b ? e b ? f b ? g
3
a
b
h
d
0.3
0.9
c
1
0.5
2
1.3
0.8
0.7
1.1
j
i
e
1
0
0
1
2
3
4
5
53
The Broadcast Incremental Power Algorithm

• BIP is similar in principle to Prims algorithm.
• One fundamental difference
• The inputs to Prims algorithm are the link cost
  Pij.
• BIP must dynamically update the costs at each
  step.

54
Conclusions

• Propose a centralized algorithm The Broadcast
  Incremental Power(BIP) Algorithm
• Advantages
• Improved performance can be obtained when
  exploiting the properties of the wireless medium
• Energy-efficient

55
Outline

• 5.1. Motivation and Goals
• 5.2. Power Control and Energy Conservation
• 5.3. Tree Topology
• 5.4. k-hop Connected Dominating Set
• 5.5. Adaptive node activity
• 5.6. Conclusions

56
Connected Dominating Set

• Connected dominating set (CDS) - construct a
  virtual backbone.
• Communicate through the virtual backbone by
  dominators.
• Example virtual backbone construction

Sensor node
57
Connected Dominating Set

• Connected dominating set (CDS) - construct a
  virtual backbone.
• Communicate through the virtual backbone by
  dominators.
• Example virtual backbone construction

1-hop Connected Dominating Set
58
Connected Dominating Set

• Connected dominating set (CDS) - construct a
  virtual backbone.
• Communicate through the virtual backbone by
  dominators.
• Example virtual backbone construction

1-hop Connected Dominating Set
2-hop Connected Dominating Set
59
A Hardness Result

• The MDS (minimum dominating set) problem is
  NP-hard, it is even a hard problem to approximate
  in general.
• For the case of unit disk graphs, it is possible
  to find a Polynomial Time Approximation Scheme
  (PTAS).

60
k-hop Connected Dominating Set
On Calculating Power-Aware Connected Dominating
Sets for Efficient Routing in Ad Hoc Wireless
Networks
Jie Wu, Fei Dai, Ming Gao, and Ivan Stojmenovic
Journal of Communications and Networks 2002
61
Introduction

• Routing based on a connected dominating set is a
  promising-approach
• Each gateway host keeps following information
  gateway domain membership list and gateway
  routing table.

3
10
11
Gateway domain member list of host 8 Gateway domain member list of host 8 Gateway domain member list of host 8
Receiver
destination member list next hop distance
9 (1,2,3,11) 9 1
4 (5,6) 7 2
7 (6) 7 1
Gateway routing table of host 8 Gateway routing table of host 8 Gateway routing table of host 8 Gateway routing table of host 8
Sender
62
Introduction

• In order to prolong the life span of each node,
  power consumption should be minimized and
  balanced among nodes.
• Unfortunately, nodes in the dominating set
  consume more energy than nodes outside the set.
• Propose a method of calculating power-aware
  connected dominating set based on a dynamic
  selection process.

5
Gateway host
6
Non-Gateway host
2
Dominated set
7
4
8
10
9
12
1
11
3
63
Network Initialization

• Every v exchanges its neighbor set N(v) with all
  its neighbors.
• Each node has two-hop neighbors information.
• Every v is marked if there exist two unconnected
  neighbors

25
64
Gateways Selection
Gateways Selection (Rules 1 and 2)
65
Gateways Selection (by applying Rule 1)

• Rule 1 Consider two vertices v and u in G. If
  Nu ? Nvin G and id( u ) lt id(v), the marker v
  is unmarked, i.e., G' is changed to G' - u.

id N(id)
21 22, 23, 24
22 20, 21, 23, 24, 25, 26, 27
66
Gateways Selection (by applying Rule 2)

• Rule 2 Assume that u and w are two marked
  neighbors of marked vertex u in G. If N(u) ?
  N(v) ? N(w) in G and id(u) minid(v),id(u),id(
  w),then the marker of u is unmarked.

id N(id)
2 1, 3, 4, 5, 6, 7, 8, 9
4 1, 2, 3, 9, 10, 11
9 2, 4, 5, 6, 7, 8, 10
67
Extended Rules

• Several extended approaches for selective removal
• The node-degree-based approach aims at reducing
  the size of the connected dominating set
• The energy-level-based approach tries to prolong
  the average life span of each node.

68
Node-degree-based Approach (Rule 3)

• Rule 3 Consider two marked vertices v and u in
  G. The marker v is unmarked if one of the
  following conditions holds
• Nu ? Nv in G and nd(u) lt nd(v)
• Nu ? Nv in G and id(u) lt id(v) when nd(u)
  nd(v), where nd() returns node degree.

id nd(id) N(id)
21 3 22,23,24
22 7 20,21,23,24,25,26,27
27 3 22,25,26
69
Node-degree-based Approach (Rule 4)

• Rule 4 Assume that u and w are two marked
  neighbors of marked vertex v in G . The marker v
  is unmarked if one of the following conditions
  holds
• Case 1. N(u) ? N(v) ? N(w), but N(v) ? N(u) ?
  N(w) and N(w) ? N(u) ? N(v) in G.

13
12
N(18) ? N(11) ? N(20) but N(11) ? N(18) ?
N(20) N(20) ? N(11) ? N(18)
id N(id)
11 4,12,13,15,16,17,18,20
18 11,17,19,20
20 11,18,19,22
15
11
16
17
4
18
20
19
22
70
Node-degree-based Approach (Rule 4)

• Rule 4
• Case 2. N(u) ? N(v) ? N(w) and N(v) ? N(u) ?
  N(w), but N(w) ? N(u) ? N(v) in G and one of
  the following conditions holds (a) nd(u) lt
  nd(v)(b) nd(u) nd(v) and id(u) lt id(v)

3
1
11
5
2
id nd(id) N(id)
2 8 1, 3, 4, 5, 6, 7, 8, 9
4 6 1, 2, 3, 9, 10, 11
9 7 2, 4, 5, 6, 7, 8, 10
4
6
10
7
9
8
71
Node-degree-based Approach (Rule 4)

• Rule 4
• Case 3. N(u) ? N(v) ? N(w), N(v) ? N(u) ? N(w)
  and N(w) ? N(u) ? N(v) in G marker u should be
  unmarked if one of the following conditions
  holds (a) nd(u) lt nd(v) and nd(u) lt nd(w)
  (b) nd(u) nd(v) lt nd(w) and id(u) lt
  id(v)(c) nd(u) nd(v) nd(w) and id(u)
  minid(v), id(u), id(w)

14
id nd(id) N(id)
11 8 4,12,13,15,16,17,18,20
13 4 11,12,14,15
15 4 11,13,14,16
13
12
15
11
16
17
4
18
20
72
Energy-level-based Approach (Rules 5?6?7?8)

• Energy-level-based rules
• Let EL denote energy level
• Rules 5, 6
• Similar to rules 1 and 2, the only difference is
  to compare EL prior to node ID.
• Rules 7, 8
• Similar to rules 3 and 4
• The only difference when nodes u and v have the
  same EL, they compare ND prior to node ID.

73
Conclusions

• Advantages
• Overall energy consumption is balanced
• A relatively small connected dominating set is
  generated

74
Outline

• 5.1. Motivation and Goals
• 5.2. Power Control and Energy Conservation
• 5.3. Tree Topology
• 5.4. k-hop Connected Dominating Set
• 5.5. Adaptive node activity
• 5.6. Conclusions

75
Whats Adaptive Node Activity?

• Influence the topology of a graph by
• Selecting certain nodes to be turned on or
• Selecting certain nodes to be turned off
• An operation that of course also fits well into
  the context of clustering or backbone mechanisms.
• Nodes that are sources or sinks of data are
  always kept active

76
Adaptive node activity
Geography-Informed Energy Conservation for Ad Hoc
Routing
Y. Xu, J. Heidemann, and D. Estrin
ACM/IEEE MobiCom 2001
77
Introduction

• Motivation
• Nodes consume high energy during routing,
  especially during transmission
• Reduce the energy consumption in ad hoc wireless
  networks
• Increase the network lifetime
• Goal
• Identifies equivalent nodes for routing
• Based on location information
• Turns off unnecessary nodes
• Load balancing energy usage
• Lifetime of all nodes remain as long as possible

78
Geographical Adaptive Fidelity(GAF) Routing

• Distribute routing duties by electing new local
  leaders periodically.
• Leaders (active nodes) handle all routing
  traffic, allowing other nodes to sleep for
  extended periods of time and conserve energy.

79
Determining Node Equivalence

• The physical space is divided into equal size
  squares.
• Based on radio communication range
• Any two nodes in adjacent squares can communicate
  with each other.
• In each grid, one node will stay in active state.

rthe length of each grid Rcommunication range
of sensor node
80
GAF State Transitions

• GAF consists of three states
• Discovery Due to mobility, node in this state
  aims to discover all nodes in the same grid
• Active In each grid, one node will stay in
  active state
• Sleeping In a grid, all nodes except the active
  node will stay in sleeping state

81
GAF State Transitions

• Initially nodes start in the Discovery state
• Node turns on its radio and find the other nodes
  within the same grid.
• The node finish the discovery duration Td,
  broadcasts its discovery message (node id, grid
  id, estimated node active time, and node state)
  and enters Active state.
• Td random 0 constant
• The other node switches its state into Sleeping
  state after receive the discovery message sentby
  the node which has higher rank value then itself.

b
c
a
d
82
Node Ranking Rule

• Given any two node i and j
• Ranki gt Rankj , if and only if (enati gt enatj)
• enat estimated node active time duration
• (enlt
  expected node lifetime)

If nodes lifetime is less than a threshold, stay
active state until energy exhaustion.
If nodes lifetime is larger than a threshold,
balancing the remain energy to avoid frequent
switches between active/sleep states.
83
GAF State Transitions

• A node in the Sleeping state wakes up after an
  application-dependent sleep time Ts, and switches
  its state into Discovery state.
• Avoiding the active node leaving the grid and
  energy unbalance.
• Ts random enat/2 enat

b
Switches to Discovery state after Ts
c
a
Energy drain
d
Larger remain energy, higher rank
84
GAF State Transitions

• The active node periodically rebroadcasts its
  discovery message
• The active node leave active state
• After the time duration Ta enat.
• Receiving discovery message send by the other
  node which has higher rank value than itself.

b
c
a
Receiving discovery message Switches to Discovery
state
Larger remain energy, higher rank Broadcasts its
discovery message Become the active node
d
85
Conclusions

• GAF increases the network lifetime without
  decreases the performance substantially
• Distribute routing duties by electing new local
  leaders periodically
• All nodes remain up for as long as possible

86
Conclusions

• Various approaches exist to adjust the topology
  of a network to a desired shape
• Most of them produce some non-negligible overhead
• Some distributed coordination among neighbors
  require additional information.
• Constructed structures can turn out to be
  somewhat brittle and the overhead might be
  wasted.
• Benefits have to be carefully weighted against
  risks for the particular scenario at hand

87
References

• R. Ramanathan and R. Rosales-Hain. Topology
  Control of Multihop Wireless Networks using
  Transmit Power Adjustment. In Proceedings of IEEE
  Infocom, pages 404413, Tel-Aviv, Israel, March
  2000
• N. Li, J. C. Hou, and L. Sha. Design and Analysis
  of an MST-Based Topology Control Algorithm. In
  Proceedings of IEEE INFOCOM, San Francisco, CA,
  March 2003
• J. Wieselthier, G. Nguyen, and A. Ephremides, On
  the Construction of Energy-Efficient Broadcast
  and Multicast Trees in Wireless Networks, in
  Proc. IEEE Infocom2000, Tel Aviv, Israel, pp.
  585594, 2000
• Jie Wu, Fei Dai, Ming Gao, and Ivan Stojmenovic,
  On Calculating Power-Aware Connected Dominating
  Sets for Efficient Routing in Ad Hoc Wireless
  Networks, Journal of Communications and Networks,
  vol. 4, No. 1, march 2002
• B. Chen, K. Jamieson, H. Balakrishnan, and R.
  Morris. Span An Energy-Efficient Coordination
  Algorithm for Topology Maintenance in Ad Hoc
  Wireless Networks. Wireless Networks, 8(5)
  481494, 2002
• Y. Xu, J. Heidemann, and D. Estrin.
  Geography-Informed Energy Conservation for Ad Hoc
  Routing. In Proceedings of the 7th Annual
  International Conference on Mobile Computing and
  Networking (MobiCom), pages 7084, Rome, Italy,
  July 2001. ACM.)