Chapter 5 To T pology C o C ntrol

Chapter 5 Topology Control

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

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 Networks can be too dense too many nodes in close (radio) vicinity

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,

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

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

Options for topology control Topology control Flat network All nodes have essentially same role Hierarchical network Assign different roles to nodes and then control node/link activity Power control Hybrid Tree Clustering Dominating sets Adaptive node activity

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

Introduction of Power Control Power control The transmitter s power can be adjusted dynamically over a wide range Typical radio adjusts their transmitter s power based on received signal strength Connected Disconnected B C D A Controls the transmitted power Topology control for desired connectivity Compensate topology changes incurred by mobility and dead nodes Controls a node s neighborhood

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

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

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

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

Introduction of Power Control Interactions Adjusting the power of A can improve the spatial reuse B C C B Interference A D E D Destination A Source Large Power makes Small Power creates more Performance Degradation Spatial Reuse Opportunities Power control B C Different Power makes Load Unbalancing D Destination Large Battery makes Longer Lifetime Small Power causes More Retransmissions Eb/No Error performance A Source A consumes much more power than C Large power, small error rate Battery drain db

Introduction of Power Control Targets and Issues Improve network throughput Improve transmission range Improve fairness Improve connectivity Neighbor discover Reduce overall energy consumption Reduce packet latency Power control helps in scheduling Reduce the interference and energy consumption Partial combination of above targets Etc.

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

Introduction Topology The set of communication links between node pairs used by routing mechanism Uncontrollable factor: Mobility, Weather, Interference, Noise Controllable factor: Transmitted power, Antenna direction

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

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

Goals Consider transmitted power adjustment problem in a multi-hop wireless network to create a desired topology

Static Networks: Min-Max Power Algorithm Static Networks: Min-Max Power Algorithm

Min-Max Power Algorithm Connected Networks Goal Find a per-node minimal assignment of transmitted power p such that (1) the induced graph is connected (2) max p is minimum

Min-Max Power Algorithm Connected Networks Phase I: CONNECTION Construct a Minimum cost spanning tree 3 3 E 4 F 3 3 13 C 2 D 31 1 1 21 A 2 B 12 Successful transmit power between i and j p = γ ( d( l, l )) + s ij i j s : the receiver sensitivity γ ( d( l, l )) i j : path loss between i and j l i : the location of node i

Min-Max Power Algorithm Connected Networks Phase II : Per Node Minimizing Power 3 3 E 4 F side-effect-edge : The edge of (C, D) is automatically connected 3 3 13 C 2 D 31 1 1 BA has a path to AB via DC with smaller power B A adjusts the transmitted power from 2 to 1. 2 1 A 2 B 12 1 The edge (A, B) can be disconnected to save more energy

Min-Max Power Algorithm Bi-Connectivity Augmentation Goal Find a per-node minimal assignment of transmit powers p such that (1) the induced graph is bi-connected (2) max p is minimum

Min-Max Power Algorithm Bi-Connectivity Augmentation Phase I: BICONN-AUGMENT Construct a Connected Minimum cost spanning tree 3 3 Successful transmit power E 4 F between i and j 13 C 2 D 13 1 1 21 A 3 3 2 B 12 p = γ ( d( l, l )) + s ij i j s : the receiver sensitivity γ ( d( l, l )) i j : path loss between i and j l i : the location of node i

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 Bi-Connected component of C component of D 3 3 E 4 F E F C D 3 3 2 A 13 C D 31 C D 1 1 21 A 2 B 12 Bi-Conn. Comp. of C Bi-Conn. Comp. of D => Add (C, D) B

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 3 3 E 4 F E Bi-Connected component of F F 3 3 13 C 2 D 31 C D 1 1 21 A 2 B 12 Bi-Conn. Comp. of E Bi-Conn. Comp. of F => Add (E, F)

Min-Max Power Algorithm Bi-Connectivity Augmentation Phase II: Per Node Minimizing Power No side-effect-edge Finish 3 3 E 4 F 3 3 13 C 2 D 31 1 1 21 A 2 B 12

Min-Max Power Algorithm Bi-Connectivity Augmentation Phase II: Per Node Minimizing Power An other example has side-effect-edge 1 3 12 3 A 1 B 3 3 3 2 side-effect-edge : The edge of (A, D) is automatically connected C 2 D 23 3 Disconnect the edge (A, B) and still Bi-Connectivity C adjusts the transmitted power from 3 to 2

Min-Max Power Algorithm Bi-Connectivity Augmentation Phase II: Per Node Minimizing Power An other example has side-effect-edge 1 3 12 32 Disconnect the edge (B, D) and still Bi-Connectivity A 1 B B adjusts the transmitted power from 3 to 2 3 2 3 3 C 2 D 2 3

Min-Max Power Algorithm Bi-Connectivity Augmentation Phase II: Per Node Minimizing Power Finish 1 3 12 32 A 1 B 3 2 3 3 C 2 D 2 3

Mobile Networks: Distributed Heuristic Algorithms Mobile Networks: Distributed Heuristic Algorithms

Mobile Networks: Distributed Heuristic Algorithms In a mobile wireless network, the topology is constantly changing Continually re-adjust the transmitted powers of nodes to maintain the desired topology Only local information since updating global information such as positions of all nodes requires prohibitive control overhead Distributed Heuristic Algorithms LINT (Local Information No Topology) LILT (Local Information Link-state Topology)

LINT (Local Information No Topology) Goal LINT uses locally available neighbor information collected by a routing protocol, and attempts to keep the degree (number of neighbors) of each node bounded

LINT (Local Information No Topology) Periodically, the node checks the number of active neighbors (degree) Attempt to keep degree of each node bounded Low threshold d l Desired node degree High threshold d h Assume : d l =2, d h =4 Degree = 31 5 < > d lh A C Nodes B and C move out the communication range of node A If degree of node A < d l Node A increases transmit power E B D Nodes D and E move in the communication range of node A If degree of node A > d h Node A decreases transmit power How node A adjusts its power?

LINT (Local Information No Topology) Node A calculates the new power periodically d = D π r c d = D π r d 2 c 2 d Path loss rc pc ( γ ( rthr ) + 10 ε log( )) = T rthr rd pd ( γ ( rthr ) + 10 ε log( )) = T r New power dd pd = pc 5 ε log( ) d r c c = thr dc dd, rd = D π D π Sign d c d d D r c r d P c P d T Current degree Desired degree Meaning Network density The communication rang with power p c The communication rang with power p d Current successful transmitted power Desired successful transmitted power The receiver sensitivity

LINT (Local Information No Topology) Disadvantages of LINT Unaware of network connectivity Danger of a network partitioning

LINT (Local Information No Topology) Disadvantage of LINT: Danger of a network partitioning Assume threshold bounds: d l =2, Low threshold d l Desired node degree High threshold d h d h =4 Degree = 3 Degree = 3 Network partitioning Since each group satisfies the condition of threshold bounds, LINT do nothing even the network is partitioned

LINT (Local Information No Topology) Disadvantage of LINT: unaware of network partitioning Example: Assume threshold bounds: d l =2, d h =4 Node A periodically checks the number of active neighbors (degree) d l d h = 2 d h Degree of A is 2 Disconnected B => No action Nodes B and C move randomly A C Disconnected Network topology change: Degree of A is 2, satisfying the threshold bounds. Network partitioning, but no action of LINT

LILT (Local Information Link-state Topology) Goal To overcome the shortcoming of LINT To exploit global connectivity information gained from routing protocols based on the link-state approach for recognizing and repairing network partitions

LILT (Local Information Link-state Topology) Aims to improve the disadvantages of LINT LILT consists of two main parts Neighbor reduction protocol (NRP) LINT mechanism Neighbor addition protocol (NAP) Triggered whenever an event driven or periodic link-state updates arrives NRP:LILT utilizes LINT mechanism to keep the desired degree of each node. NAP:For recognizing and repairing network partitions.

LILT- Neighbor Addition Protocol (NAP) Current topology state Disconnected The node uses its largest transmitted power Connected but not Bi-connected If is still not Bi-connected after time t, the node uses its largest transmitted power Node B and C move randomly Disconnected B A C Connected Disconnected Node A uses its largest transmitted power

LILT- Neighbor Addition Protocol (NAP) Current topology state Disconnected The node uses its largest transmitted power Node B and C move randomly Connected but not Bi-connected If A is still not Bi-connected after time t, the node uses its largest transmitted power Node B and C move randomly Disconnected B Not Bi-connected B A Connected C A C Connected Disconnected Node A uses its largest transmitted power Node A waiting for a time period. If still not Bi-connected, node A uses its largest transmitted power

Conclusions The paper considered the problem of adjusting the powers of nodes in a multi-hop wireless network to create a desired topology Propose power control mechanism for static networks to maintain Connected Bi-connected Propose two mechanisms for mobile networks: LINT and LILT.

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

Introduction of Tree Topology Control Example: MPR (Multi-Point Relay) election Retransmission node (a) (b) is better Retransmission node (b)

Introduction of Tree Topology Control Example: a a b c b c d e f d e f g h g h (a) a to d needs 2 hops (b) a to d needs 7 hops (a) is better

Tree Topology Design and Analysis of an MST-Based Topology Control Algorithm N. Li, J. C. Hou, and L. Sha IEEE INFOCOM 2003

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 B B I I C F C F A D G H A D G H E E (1) No Topology Control (2) With Topology Control

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

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

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. Maximal Transmission Power a b u s ID and Location u c d

LMST Step1: Information Collection Information Exchange Since Hello message includes the node s ID and Location, after obtaining the Hello message of 1-hop neighbors, node u can construct the local view. a b u c d

LMST Step2: Topology Construction Each node uses location information of its neighbor can estimate their distance 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 r c : Coefficient c d, r 2 d : distance Decrease the transmission range can conserve the power of squared times 7 a 7 5 6 e u 5 6 b 7 10 3 c 4 d

LMST Step2: Topology Construction Each node applies Prim s algorithm independently to obtain its Local Minimum Spanning Tree. Node u constructs the Local Minimum Spanning Tree using Prim s 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. Small power Creates more Spatial Reuse Opportunities Decreases energy consumption u 7 3 a 5 c 7 5 6 b 6 7 4 d 10 e

LMST Step3: 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 P = Two-Ray P 2 PG t tgrλ ( 4πd ) L r 2 PG t tgrh = d L r 2 2 t h 2 r Sign P t P r G t G r λ d L h t h r Transmit power Receive power Meaning Antenna gain of the transmitter Antenna gain of the receiver Wave length Distance between nodes System loss Antenna height of the transmitter Antenna height of the receiver

LMST Step3: Determination of Transmission Power In general, the relation between P r and P t is of the following form 2 G G P P G Where G is a function of r = t t r λ 2 ( 4πd ) L

LMST Step3: Determination of Transmission Power In general, the relation between P r and P t is of the following form 2 G P P G Where G is a function of r = t t G r λ 2 ( 4πd ) L Example P th is the required power threshold to successfully receive the message P max is the maximal transmission power e Node b will compute: a G = P r / P max b Node b transmits data to u: Pth G = P th P r / P max u c Hello Data d Data with P th G Hello with P max

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

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

Introduction The paper studies the problems of broadcasting and multicasting in wireless networks. Previously developed models for multicasting are based on link-based models Do not reflect the properties of the wireless network environment.

Goals To form a minimum-energy tree Energy efficiency Maintain network connectivity

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.

Wireless Communications Model Node-based transmission cost evaluation P i,(j,k) = max{p ij, P ik } P ij : Transmission power for node i to transmit packets to node j P ij P ik > P ij j The larger power (P ik ) can cover both of node j and node k The smaller power (P ij ) can only cover node j i P ik k

Minimum-Energy Broadcast Tree Construction Minimum-Energy Broadcast Tree Construction

Basic Concept P ij = r 2 (r :transmission range) b b Source 30 3 2.5 1.5 a 5.2 3 120 Source 3 a Power consumption: Source b: 3 2 = 9 Power consumption: Source b: 3 2 = 9 Minimum cost (Source a b): 2.5 2 +1.5 2 = 8.5 Minimum cost (Source a b): 3 2 +5.2 2 = 36.04

Minimum-Energy Broadcast Tree Construction - Minimum-Energy Broadcasting: 2 Destinations Strategy (a): S D 2 Strategy (b): D 2 r 2 S θ S D 1 D 2 r 2 θ S D 1 θ = 90 θ > 90 r 1 r 12 D 1 D 2 r 1 θ r 12 r 12 D 2 S D 1 (r 2 ) 2 < (r 1 ) 2 +(r 12 ) 2 (r 2 ) 2 < (r 1 ) 2 +(r 12 ) 2 Apply Strategy (a) r 2 r 1 Apply Strategy (a) r 1 > r 2 cosθ θ θ < 90 r 2 r 1 D 2 r 12 S D 1 (r 2 ) 2 < (r 1 ) 2 +(r 12 ) 2 Apply Strategy (a) Otherwise θ r 1 r 2 S D 1 (r 2 ) 2 > (r 1 ) 2 +(r 12 ) 2 D 2 r 12 Apply Strategy (b)

Minimum-Energy Broadcast Tree Construction - Minimum-Energy Broadcasting: 2 Destinations Strategy (a): S D 2 Strategy (b): S D 1 D 2 D 2 r 2 r 12 θ S D 1 r 1 Decision: If θ 90 : apply Strategy (a) Otherwise: If r 1 > r 2 cosθ: apply Strategy (a) Otherwise: apply Strategy (b)

Minimum-Energy Broadcast Tree Construction - Minimum-Energy Broadcasting: 2 Destinations The complexity of this formulation is high, making it impractical except for small networks. (N D :number of destinations) N D =10, more than 51,000 calls are needed. N D = 13, more than 14 million calls are needed.

Broadcast Incremental Power Algorithm Broadcast Incremental Power Algorithm

Network Assumptions Rooted at the Source, that reaches all of the desired destinations Initially, the tree consists of only the Source.

The Broadcast Incremental Power Algorithm 5 4 3 2 1 f d e 1.2 1 b 0.3 a 1.5 0.5 1.7 1.3 1.1 0.7 j c g 0.9 0.8 1.3 i h Assume node a is the source node Step 1: Determining the node that the Source can reach with minimum expenditure of power. a 0.3 b 0 0 1 2 3 4 5 a 0.5 c

The Broadcast Incremental Power Algorithm 5 4 3 2 1 0 f d e 1.2 1.5 b a 0.3 1 0.5 1.7 1.3 1.1 0.7 j g 1.3 0 1 2 3 4 5 c 0.9 0.8 i h Step 2: Determine which new node can be added to the tree at minimum additional cost. P ac a P 0.3 a a 0.5 b P a P a = 0.5 0.3 = 0.2 Minimum additional cost P bd P b b b P b = 1 0 = 1 P b 1 c d

The Broadcast Incremental Power Algorithm 5 4 3 2 1 f d e 1.2 b a 1.5 0.3 1 0.5 1.1 1.7 c g 0.9 1.3 1.3 0.8 0.7 j i h Step 2: Determine which new node can be added to the tree at minimum additional cost. P aj a P 0.5 a a 1.3 P a = 1.3 0.5 = 0.8 P cj P c c P c 0.7 c P a c Minimum additional cost P c = 0.7 0 = 0.7 j j 0 0 1 2 3 4 5 P bd P b P b b 1 b P b = 1 0 = 1 d

The Broadcast Incremental Power Algorithm 5 4 3 2 1 f d e 1.2 b a 1.5 0.3 1 0.5 1.1 1.7 c g 0.9 1.3 0.8 0.7 j Step 2: Determine which new node can be added to the tree at minimum additional cost. 1.3 And so forth: i h c i c h b d b e b f b g 0 0 1 2 3 4 5

The Broadcast Incremental Power Algorithm BIP is similar in principle to Prim s algorithm. One fundamental difference: The inputs to Prim s algorithm are the link cost P ij. BIP must dynamically update the costs at each step.

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

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

Connected Dominating Set Connected dominating set (CDS) - construct a virtual backbone. Communicate through the virtual backbone by dominators. Example: virtual backbone construction Sensor node

Connected Dominating Set Connected dominating set (CDS) - construct a virtual backbone. Communicate through the virtual backbone by dominators. Example: virtual backbone construction Sensor node Dominators CDS edge Virtual backbone 1-hop Connected Dominating Set

A hardness result The MDS problem is NP-hard, it is even a hard problem to approximate in general graphs as it not even approximable within c log V for some c > 0. For the case of unit disk graphs, it is possible to find a Polynomial Time Approximation Scheme (PTAS).

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

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 Receiver 2 9 5 4 7 6 Gateway host Non-Gateway host dominated set 10 11 Gateway domain member list of host8 1 8 10 Sender destination member list next hop distance 9 (1,2,3,11) 9 1 3 11 4 (5,6) 7 2 7 (6) 7 1 Gateway routing table of host8

Introduction Finding a minimum connected dominating set is NP for most graphs Find a simple distributed algorithm that can quickly determine a relatively small connected dominating set is important.

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. 5 6 Gateway host 2 4 7 Non-Gateway host dominated set 9 8 10 1 12 3 11 Propose a method of calculating power-aware connected dominating set based on a dynamic selection process.

Network Initialization Every v exchanges its open 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 12 13 14 Become a Gateway host 15 unconnected 1 3 11 16 5 2 4 17 6 7 8 9 10 21 20 22 18 27 19 Gateway host Non-Gateway host 23 24 25 26

Gateways Selection Gateways Selection (Rules 1 and 2)

Gateways Selection (by applying Rule 1) Rule 1: Consider two vertices v and u in G. If N[v] N[u]in G and id( v ) < id(u), the marker v is unmarked, i.e., G' is changed to G' - {U}. N(21) N(22) 20 id N(id) 21 22, 23, 24 21 22 27 22 20, 21, 23, 24, 25, 26, 27 23 24 25 26 Gateway host Non-Gateway host

Gateways Selection (by applying Rule 2) Rule 2: Assume that u and w are two marked neighbors of marked vertex v in G. If N(v) N(u) N(w)in G and id(v) = min{id(v),id(u),id( w)},then the marker of v 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 6 5 N(2) N(4) N(9) and id(2) = min{id(2), id(4), id(9)} 2 1 3 4 11 7 8 9 10 Gateway host Non-Gateway host

Extended Rules Extended Rules

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.

Node-degree-based approach 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: N[v] N[u] in G and nd(w) < nd(u) N[v] N[u] in G and id(v) < id(u) when nd(v) = nd(u), 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 N(21) N(22) and nd(21)=3 < nd(22)=6 20 N(27) N(22) nd(27)=3 < nd(22)=6 21 22 27 23 24 25 26 Gateway host Non-Gateway host

Node-degree-based approach 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(v) N(u) N(w), but N(u) N(v) N(w) and N(w) N(u) N(v) in G. 13 id N(id) 12 N(18) N(11) N(20) 11 4,12,13,15,16,17,18,20 18 11,17,19,20 20 11,18,19,22 11 15 16 N(18) N(11) N(20) but N(11) N(18) N(20) N(20) N(11) N(18) 4 18 17 20 22 19 Gateway host Non-Gateway host

Node-degree-based approach Approach (Rule 4) Rule 4: Case 2. N(v) N(u) N(w) and N(u) N(v) N(w), but N(w) N(u) N(v) in G; and one of the following conditions holds: (a). nd(v) < nd(u) (b). nd(v) = nd(u) and id(v) < id(u) 1 3 11 id nd(id) N(id) 2 8 1, 3, 4, 5, 6, 7, 8, 9 4 6 1, 2, 3, 9, 10, 11 5 6 2 4 9 7 2, 4, 5, 6, 7, 8, 10 7 9 10 N(2) N(4) N(9) N(9) N(2) N(4) but N(4) N(2) N(9) nd(9)=7 < nd(2)=8 8 Gateway host Non-Gateway host

Node-degree-based approach Approach (Rule 4) Rule 4: Case 3. N(v) N(u) N(w), N(u) N(v) N(w) and N(w) N(u) N(v) in G; marker v should be unmarked if one of the following conditions holds: (a) nd(v) < nd(u) and nd(v) < nd(w) (b) nd(v) = nd(u) < nd(w) and id(v) < id(u) (c) nd(v) = nd(u) = nd(w) and id(v) = min{id(v), id(u), id(w)} id nd(id) N(id) N(13) N(11) N(15) 11 8 4,12,13,15,16,17,18,20 N(15) N(11) N(13) 14 12 13 but 13 4 11,12,14,15 N(11) N(13) N(15) 15 4 11,13,14,16 15 nd(13) = nd(15) = 4 11 16 id(13) < id(15) 4 18 17 Gateway host 20 Non-Gateway host

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 v and u have the same EL, they compare ND prior to node ID.

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

k-hop Connected Dominating Set Span: An Energy-Efficient Coordination Algorithm for Topology Maintenance in Ad Hoc Wireless Networks B. Chen, K. Jamieson, H. Balakrishnan, and R. Morris ACM Wireless Networks Journal 2002

Introduction A dense sensor network can work with only part of all nodes being active It is possible to prolong the network lifetime while maintain its functionality by carefully choosing the active nodes

Goal Reduce the energy consumption in sensor networks It should allows as many nodes as possible to turn their radio off Routing efficiency can be guaranteed

The Essential Ideas of SPAN non-coordinator node coordinator node Destination Doesn t relay packets Relay packets Source

Coordinator Eligibility Rule If two neighbors of a non-coordinator node cannot reach each other directly or via one or two coordinators, the node should become a coordinator non-coordinator node 1 2 1 2 coordinator node 3 4 3 4 5 5 6 6 7 Non-coordinator nodes 1 and 6 cannot reach each other directly or via one or two coordinators Become a coordinator node All of the non-coordinator neighbors of node 4 can reach each other directly or via one or two coordinators Not become a coordinator node

Coordinator Contention 1 2 1 2 1 2 3 4 5 3 4 5 3 4 5 6 7 6 7 6 7 Initial configuration All the nodes are eligible And try to be a coordinator at the same time 1 Boo 2 3 Boo 4 Boo 5 Announcement Contention 6 7

Resolving Announcement Contention - using backoff delay C i : Number of additional pairs among the neighbors that can be connected ( ) P i = N i : Number of neighbor pairs 2 Ci = (( 1 ) + R) Ni T Large additional pairs, P Small delay time R : A random number N i : Number of neighbors for node i T : Time unit i b a d c P d = N 2 d 3 = = 3 2 If node d becomes a coordinator node, the additional pairs are (a,b) and (a, c) f e h g = C d =2 C h =0 delay d = ((1-2/3) + R) 3 T Node d has smaller delay P d N 2 d 3 = = 3 2 If node h becomes a coordinator node, no additional pair (all of the neighbors are already connected) delay h = ((1-0/3) + R) 3 T

Resolving Announcement Contention - with Energy concern delay Er Ci = ((1 ) + (1 ) + R) Ni T E P m E r : the amount of energy at a node that still remains E m : the maximum amount of energy available at the same node Large remain energy, Small delay time i

Coordinator Withdrawal Rules Every pair of its neighbors can reach other either directly or via some other coordinators Become a non-coordinator node 1 2 1 2 3 4 5 3 4 5 6 7 6 7 nodes1 and node5:can reach each other via coordinator 2 nodes5 and node7:can reach each other directly nodes1 and node7:can reach each other via coordinator3 and coordinator6

Conclusions Advantages Energy-Efficient Prolong the network life time

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

What s 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

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

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

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.

Determining Node Equivalence The physical space is divided into equal size squares. Based on nominal radio range Any two nodes in adjacent squares can communicate with each other. In each grid, one node will stay in active state. 2r Destination R r r r R 5 r r r:the length of each grid R:communication range of sensor node Active node Sleeping node Source r r r

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 Sleeping Discovery After Td After Ta Active

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. b Td = random [0 ~ constant] The other node switches its state into Sleeping state after receive the discovery message send by the node which has higher rank value then itself. a 75% 54% d c 92% 23% :sleeping state :discovery state :active state

Node Ranking Rule Given any two node i and j Rank i > Rank j, if and only if (enat i > enat j ) enat = estimated node active time duration (enlt = expected node lifetime),when enlt larger than a threshold,when enlt becomes less than a threshold If node s lifetime is less than a threshold, stay active state until energy exhaustion. If node s lifetime is larger than a threshold, balancing the remain energy to avoid frequent switches between active/sleep states.

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] Larger remain energy, Higher rank Switches to Discovery state after Ts a 75% b 54% d c 70% 92% Energy drain 23% :sleeping state :discovery state :active state

GAF State Transitions The active node periodically rebroadcasts its discovery message. The active node leave active state if After the time duration enat. Receiving discovery message send by the other node which has higher rank value then itself. b a 54% c Larger remain energy, Higher rank Broadcasts its discovery message Become the active node 75% d 23% 70% Receiving discovery message Switches to Discovery state :sleeping state :discovery state :active state

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

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

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

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