Topology Control

Murat Demirbas

SUNY Buffalo

Uses slides from

Y.M. Wang

and A. Arora

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• High density deployment is common

• Even with minimal sensor coverage, we get a high density communication network (radio range > typical sensor range)

• Energy constraints

• When not easily replenished

• High interference

• Many nodes in communication range

We will look at selecting high-quality links as part of routing!

Why Control Communications Topology

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Problem Statement(s)

1. Choose a transmit-power level whereby network is connected

• per node or same for all nodes

• with per node there is the issue of avoiding asymmetric links

• cone-based algorithm:

node u transmits with the minimum power ρu s.t. there is at least one neighbor in every

cone of angle x centered at u

2. Find an MCDS, i.e. a minimum subset of nodes that is both:

Set cover

Connected

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Problem Statement(s)

3. Find a minimum subset of nodes that provides some density

in each geographic region connectivity we’ll look at the examples of SPAN, GAF, CEC

Sub-problems:

• Prune asymmetric links• Tolerate node perturbations• Load balance

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Outline

• Cone-based algorithm

• SPAN

• GAF-CEC

Analysis of a Cone-Based Distributed Topology Control Algorithm for Wireless Multi-hop Networks

L. Li, J. Y. HalpernCornell University

P. Bahl, Y. M. Wang, and R. WattenhoferMicrosoft Research, Redmond

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OUTLINE

• Motivation

• Bigger Picture and Related Work

• Basic Cone-Based Algorithm

Summary of Two Main Results

Properties of the Basic Algorithm

• Optimizations

Properties of Asymmetric Edge Removal

• Performance Evaluation

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• Example of No Topology Control with maximum transmission radius R (maximum connected node set)

High energy consumption High interference Low throughput

Motivation for Topology Control

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Network may partition

• Example of No Topology Control with smaller transmission radius

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Global connectivity Low energy consumption Low interference High throughput

• Example of Topology Control

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Bigger Picture and Related Work

Routing

MAC / Power-controlled MAC

SelectiveNode

Shutdown

TopologyControl

Relative Neighborhood Graphs, Gabriel graphs, Sphere-of-Influence graphs, -graphs, etc.

[GAF][Span]

[Hu 1993][Ramanathan & Rosales-Hain 2000][Rodoplu & Meng 1999][Wattenhofer et al. 2001]

ComputationalGeometry

[MBH 01][WTS 00]

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Basic Cone-Based Algorithm (INFOCOM 2001)

• Assumption: receiver can determine the direction of sender

Directional antenna community: Angle of Arrival problem

• Each node u broadcasts “Hello” with increasing power (radius)

• Each discovered neighbor v replies with “Ack”.

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Cone-Based Algorithm with Angle

Need a neighbor in every -cone.

Can I stop?

No! There’s an -gap!

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Notation

• E = { (u,v) V x V: v is a discovered neighbor by node u}

G = (V, E)

E may not be symmetric

(B,A) in E but (A,B) not in E

R A B 70

60

50

= 145

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Two symmetric sets

• E+ = { (u,v): (u,v) E or (v,u) E }

Symmetric closure of E

G+ = (V, E

+ )

• E- = { (u,v): (u,v) E and (v,u) E }

Asymmetric edge removal

G- = (V, E

- )

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Summary of Two Main Results

• Let GR = (V, ER), ER = { (u,v): d(u,v) R }

• Connectivity Theorem

If 150, then G+ preserves the connectivity of GR and the bound is tight.

• Asymmetric Edge Theorem

If 120, then G- preserves the connectivity of GR and the bound is tight.

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The Why-150 Lemma

150 = 90 + 60

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Both circles have max radius R

A

N

B

• Counterexample for = 150 +

Properties of the Basic Algorithm

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Both circles have max radius R

A

W

N

K

J

B

Y

WAN = 150 WAK = 150

• Counterexample for = 150 +

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Both circles have max radius R

A

N

B W

K

J

Y

WAN = 150 WAK = 150 Z

X 150 < WAX < α

d(A,X) < R < d(X,B)

• Counterexample for = 150 +

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For 150 ( 5/6 )

• Connectivity Lemma

if d(A,B) = d R and (A,B) E+, there must be a pair of nodes, one red and one green, with

distance less than d(A,B).

A B W

Y

Z

X

d

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Connectivity Theorem

• Order the edges in ER by length and induction on the rank in the ordering

For every edge in ER, there’s a corresponding path in G+ .

• If 150, then G+ preserves the connectivity of GR and the bound

is tight.

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Optimizations

• Shrink-back operation

“Boundary nodes” can shrink radius as long as not reducing cone coverage

• Asymmetric edge removal

If 120, remove all asymmetric edges

• Pairwise edge removal

If < 60, remove longer edge e2

e1

e2

A B

C

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Properties of Asymmetric Edge Removal

• Counterexample for = 120 +

R A B

60+/3

60

60-/3

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For 120 ( 2/3 )

• Asymmetric Edge Lemma

if d(A,B) R and (A,B) E, there must be a pair of nodes, W or X and node B, with distance less than d(A,B).

A B

W

X

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Asymmetric Edge Theorem

• Two-step inductions on ER and then on E

For every edge in ER , if it becomes an asymmetric edge in G , then there’s a corresponding path consisting of only symmetric edges.

• If 120, then G- preserves the connectivity of GR and the bound

is tight.

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Performance Evaluation

• Simulation Setup

100 nodes randomly placed on a 1500m-by-1500m grid. Each node has a maximum transmission radius 500m.

• Performance Metrics

Average Radius

Average Node Degree

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Average Radius

0

100

200

300

400

500

600

Basic With opt1 Withopt1&2

With allopts

Ave

rag

e ra

diu

s

Max power

150-deg

120-deg

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Average Node Degree

0

5

10

15

20

25

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Basic With opt1 Withopt1&2

With allopts

Ave

rag

e n

od

e d

egre

e

Max power

150-deg

120-deg

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• In response to mobility, failures, and node additions

• Based on Neighbor Discovery Protocol (NDP) beacons

Joinu(v) event: may allow shrink-back

Leaveu(v) event: may resume “Hello” protocol

AngleChangeu(v) event: may allow shrink-back or resume “Hello” protocol

• Careful selection of beacon power

Reconfiguration

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• Distributed cone-based topology control algorithm that achieves maximum connected node set

If we treat all edges as bi-directional

150-degree tight upper bound If we remove all unidirectional edges

120-degree tight upper bound

• Simulation results show that average radius and node degree can be significantly reduced

Summary

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Outline

• Cone-based algorithm

• SPAN

• GAF-CEC

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SPAN

• Goal: preserve fairness and capacity & still provide energy savings

• SPAN elects “coordinators” from all nodes to create backbone topology

• Other nodes remain in power-saving mode and periodically check if they should

become coordinators

• Tries to minimize # of coordinators while preserving network capacity

• Depends on an ad-hoc routing protocol to get list of neighbors & the

connectivity matrix between them

• Runs above the MAC layer and “alongside” routing

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Coordinator Election & Announcement

• Rule: if 2 neighbors of a non-coordinator node cannot reach each other

(either directly or via 1 or 2 coordinators), node becomes coordinator

• Announcement contention is resolved by delaying coordinator

announcements with a randomized backoff delay

• delay = ((1 – Er/Em) + (1 – Ci/(Ni pairs)) + R)*Ni*T

Er/Em: energy remaining/max energy

Ni: number of neighbors for node i

Ci: number of connected nodes through node i

R: Random[0,1]

T: RTT for small packet over wireless link

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Coordinator Withdrawal

• Each coordinator periodically checks if it should withdraw as a coordinator

• A node withdraws as coordinator if each pair of its neighbors can reach each other

directly of via some other coordinators

• To ensure fairness, after a node has been a coordinator for some period of time, it

withdraws if every pair of nodes can reach each other through other neighbors (even

if they are not coordinators)

• After sending a withdraw message, the old coordinator remains active for a “grace

period” to avoid routing loses until the new coordinator is elected

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Performance Results

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Outline

• Cone-based algorithm

• SPAN

• GAF-CEC

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GAF/CEC: Geographical Adaptive Fidelity

• Each node uses location information (provided by some orthogonal

mechanism) to associate itself to a virtual grid

• All nodes in a virtual grid must be able to communicate to all nodes

in an adjacent grid

• Assumes a deterministic radio range, a global coordinate system

and global starting point for grid layout

• GAF is independent of the underlying ad-hoc routing protocol

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Virtual Grid Size Determination

• r: grid size, R: deterministic radio range

• r2 + (2r)2 <= R2

• r <= R/sqrt(5)

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Parameters settings

• enat: estimated node active time

• enlt: estimated node lifetime

• Td,Ta, Ts: discovery, active,

and sleep timers

• Ta = enlt/2

• Ts = [enat/2, enat]

• Node ranking:

Active > discovery (only one node active per grid)

Same state, higher enlt --> higher rank (longer expected time first)

Node ids to break ties

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Performance Results

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CEC

• Cluster-based Energy Conservation

• Nodes are organized into overlapping clusters

• A cluster is defined as a subset of nodes that are mutually

reachable in at most 2 hops

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Cluster Formation

• Cluster-head Selection: longest lifetime of all its neighbors

(breaking ties by node id)

• Gateway Node Selection:

primary gateways have higher priority

gateways with more cluster-head neighbors have higher priority

gateways with longer lifetime have higher priority

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Network Lifetime