algorithmic aspects of throughput-delay performance for...

Algorithmic Aspects of Throughput-Delay Performance for FastData Collection in Sensor Networks

Amitabha GhoshCommittee:

Bhaskar KrishnamachariC.S. Raghavendra

Gaurav S. Sukhatme

Autonomous Networks Research GroupMing Hsieh Department of Electrical Engineering

USC Viterbi School of [email protected]

http://anrg.usc.edu/˜amitabhg

July 27, 2010

Algorithmic Aspects of Throughput-Delay Performance for Fast Data Collection in Sensor Networks

Thesis Statement:

Multi-channel scheduling, optimal routing topologies, and transmission powercontrol are necessary in order to improve the throughput-delay trade-off foraggregated convergecast in large-scale, multi-hop, wireless sensor networks.

2 / 47


Outline

1 Maximizing Convergecast ThroughputMotivation and PreliminariesScheduling with Unlimited FrequenciesApproximations on Unit Disk GraphsApproximations on General Disk Graphs

2 Multi-Channel Scheduling in SINRMotivation and Interference ModelsProblem Formulation and ApproachApproximations in SINR

3 Throughput-Delay Trade-offMotivationBi-criteria FormulationOptimal Spanning Trees (parts)

4 Distributed Topology Control in 3-DMotivationTwo Approaches: Orthographic Projections, SDT

3 / 47


Maximizing Convergecast Throughput

Outline



3 Throughput-Delay Trade-offMotivationBicriteria FormulationOptimal Spanning Trees

4 Conclusions

4 / 47



Motivation and Preliminaries

Model and Assumptions

Secondary conflict

e.g., Applications with fast &efficient data collectionrequirements.

5 / 47




Model and Assumptions

Secondary conflict

e.g., Applications with fast &efficient data collectionrequirements.

TDMA periodic scheduling(- every node generates a single packet at thebeginning of each frame- every node transmits once per slot)

Graph-based network & interference model

Half-duplex, single transceiver

Receiver-based Frequency Assignment

Non-interfering orthogonal channels

In-network aggregation(distributive, algebraic- aggregation happens at each hop)

1 2 3 k. . .

Schedule length

5 / 47




Convergecast and Benefits of Multiple Frequencies

Convergecast

A many-to-one communication pattern (i.e., flow of data): from all the nodesto a sink (opposite of broadcast).

a b c

d e f g

s

f1 f1f1

f1

1

12

23 4

5

Figure: Schedule length is 5.

6 / 47





Convergecast


a b c

d e f g

s

f1 f1f1

f1

1

12

23 4

5


a b c

d e f g

s

f1 f1f2

f1

1

12

21 2

3


6 / 47





Convergecast


Frame 1 Frame 2

Receiver Slot 1 Slot 2 Slot 3 Slot 1 Slot 2 Slot 3

sab

c

c

de

a d

fg

bef c g

de f

a d bef

g

Pipelining

a b c

d e f g

s

f1 f1f2

f1

1

12

21 2

3


7 / 47




Problem Formulation

Joint Frequency and Time Slot Assignment

Given a connected network G = (V, E) of arbitrarilydeployed nodes, K orthogonal frequencies, and a routingtree T ⊆ G rooted at the sink s ∈ V

Assign a frequency to each receiver in T

Assign a time slot to each edge in T

such that the aggregated throughput at the sink is max-imized, where

Aggregated Throughput = 1/Schedule Length(equivalent to minimizing the Schedule Length) Secondary conflict

8 / 47




Scheduling Complexity

Theorem

Joint Frequency and Time Slot Assignment is NP-hard on general graphs.Proof: Reduction from Vertex Color.

Questions

Does the problem still remain NP-hard with unlimited frequencies?

If not, how many frequencies (at a min, or at most) are needed?

Can we design algorithms that have provable, worst-case guarantee?

9 / 47




Scheduling Complexity

Theorem

Joint Frequency and Time Slot Assignment is NP-hard on general graphs.Proof: Reduction from Vertex Color.

Questions

Does the problem still remain NP-hard with unlimited frequencies?

If not, how many frequencies (at a min, or at most) are needed?

Can we design algorithms that have provable, worst-case guarantee?

Theorem

Given a spanning tree T on a graph G = (V, E), findingthe minimum number of frequencies required to removeall secondary conflicts is NP-hard.

f1

f2

1 1

Secondary conflict

9 / 47



Scheduling with Unlimited Frequencies

A Frequency Upper Bound

Constraint Graph

For each receiver in G create a node in GC .

Create an edge between two nodes in GC if the corresponding receivers inG form a secondary conflict.

1 2

3 4 5

6 7 8

9

10 11

12 13 15 1614

s

f11 2

3 4 5

6 7 8f4

f4

f1

f2f2

f3f3

f3sLargest DegreeFirst

Lemma

Kmax ≤ ∆(GC) + 1, where ∆(GC): max degree in GC . (Vertex Color)

10 / 47




Time Slot Assignment

Algorithm: BFS-TimeSlotAssignment

1. while ET 6= φ do2. e← next edge from ET in BFS order3. Assign minimum time slot to e respecting

adjacency constraint4. ET ← ET \ {e}5. end while

1 2

3 4 5

6 7 8

9

10 11

12 13 15 1614

s

1

1

1

1

1

2 3

2

2

2 2

2

2

3 3

3

f1

f4

f4

f1

f2f2 f3

f3

f3

Theorem

BFS-TimeSlotAssignment gives a schedule of minimum length ∆(T ), where∆(T ): maximum node degree in T .

11 / 47




Evaluation

Parameters:

Number of nodes: n : 200, square region of area A : 200× 200

Shortest Path Tree, Unit Disk Graph

0 0.1 0.2 0.3 0.4 0.50

5

10

15

20

25

30

Network Density

Num

ber

of F

requ

enci

es o

n S

PT

Largest Degree FirstUpper Bound ∆(G

C) + 1

Figure: Number of frequencies required to remove all secondary conflicts as a functionof network density n/A on SPT.

12 / 47




So far...

Joint Frequency and Time Slot Assignment is

NP-hard with limited (constant number) frequencies on arbitrary graphs.

Polynomial with unlimited (at most ∆(GC) + 1) frequencies for arbitrarygraphs.

Next...

Approximation algorithms for Random Geometric Graphs with limited (constantnumber) frequencies.

Uniform transmission range (Unit Disk Graphs)

Non-uniform transmission range (General Disk Graphs)

13 / 47



Approximations on Unit Disk Graphs

Approximation on UDG

Algorithm AUDG Overview

Phase 1: Assign frequencies to thereceivers in each cell such that themaximum number of nodes transmittingon the same frequency (load) is minimized.(Load-Balanced Frequency Assignment)

Phase 2: Assign time slot greedily to eachedge.

e e�f f

g1 g1

g1 g1

g2 g2

g2 g2

g3 g3

g3 g3

g4 g4

g4 g4

a>2R

u u�v v�

e e�f f

u u�v v�

14 / 47




Approximation on UDG

Algorithm AUDG Overview

Phase 1: Assign frequencies to thereceivers in each cell such that themaximum number of nodes transmittingon the same frequency (load) is minimized.(Load-Balanced Frequency Assignment)

Phase 2: Assign time slot greedily to eachedge.

e e�f f

g1 g1

g1 g1

g2 g2

g2 g2

g3 g3

g3 g3

g4 g4

g4 g4

a>2R

u u�v v�

e e�f f

u u�v v�

Theorem

Algorithm AUDG achieves a constant factor 8µα ·(

43− 1

3K

)

approximation onthe optimal schedule length, where µα > 0 is a constant for any given cell sizeα ≥ 2R, and given node deployment, whereµα : maximum number of edges on the same frequency in any cell that can bescheduled simultaneously by any algorithm.

14 / 47




Evaluation

Parameters

UDG on a region of size 200× 200 with transmission radius R = 25

Shortest Path Tree

100 200 300 400 500 600 700 8005

10

15

20

25

30

35

40

45

50

Number of Nodes

Sch

edul

e Le

ngth

SPT, K=1SPT, K=3SPT, K=5

Observations

Schedule length decreases withincreasing number of frequencies

However, with diminishing returns

Structure of the routing tree (highnode degree) may lead tobottlenecks

15 / 47



Approximations on General Disk Graphs

Approximation on Disk Graphs

16 / 47





Notations

r(u): Transmission range of node u

ℓ(e): Length of edge e

I(e): Set of edges that are either adjacent to e or form a secondaryconflict with e

I≥(e): Subset of I(e) that have larger disks than e

I≥(e) = {e′ = (u′, v′) : e′ ∈ I(e), ℓ(e′) ≥ ℓ(e)}

euv

16 / 47





Algorithm ADG Overview

Phase 1: Assign frequencies such that the maximum number of edgesinterfering with any given edge is minimized.

0 − 1 Integer Linear Program: Define indicator variables Xvk for edgee = (u, v) as:

Xvk =

{

1, if receiver v is assigned frequency fk

0, otherwise

A frequency assignment is a 0 − 1 assignment to Xvk, ∀e, ∀fk.

17 / 47





Algorithm ADG Overview

Phase 1: Assign frequencies such that the maximum number of edgesinterfering with any given edge is minimized.

0 − 1 Integer Linear Program: Define indicator variables Xvk for edgee = (u, v) as:

Xvk =

{

1, if receiver v is assigned frequency fk

0, otherwise

A frequency assignment is a 0 − 1 assignment to Xvk, ∀e, ∀fk.

Phase 2: Sort edges in non-increasing order of lengths, and assign smallestavailable slots starting from the largest.

17 / 47





0-1 Integer Linear Program of Frequency Assignment

Minimize λ

subject to :

∀e = (u, v), ∀fk :∑

v′

n(e, v′)Xvk ≤ λ (1)

∀e = (u, v) :∑

fk

Xvk = 1, (2)

∀e = (u, v), ∀fk : Xvk ∈ {0, 1} (3)

Solve the Linear Relaxation (LP) by modifying constraint (3)

Randomized Rounding: Assign Yvk = 1 with probability X∗vk, where X∗

vk

are the optimal fractional LP solutions, and Yvk are the new integralrandom variables.

18 / 47





Lemma

Let Yvk be the rounded solution, as described above. Then,

maxe,fk

∑

e′=(u′,v′)∈I≥(e)

Yv′k

= O (∆(T ) log n · λ∗) ,

with probability at least (1− 1/n).Proof: Apply Chernoff bound.

19 / 47





Lemma

Let Yvk be the rounded solution, as described above. Then,

maxe,fk

∑

e′=(u′,v′)∈I≥(e)

Yv′k

= O (∆(T ) log n · λ∗) ,

with probability at least (1− 1/n).Proof: Apply Chernoff bound.

Theorem

The schedule constructed by time slot assignmentt strategy along with the fre-quency assignment using the above randomized rounding procedure results in aschedule of length O(∆(T ) · log n) times the optimum.

19 / 47


Multi-Channel Scheduling in SINR

Outline




4 Conclusions

20 / 47



Motivation and Interference Models

Realistic Interference Model

Limitations of a Graph-Based Model (Protocol Model)

Interference is binary and stops abruptly beyond a distance - idealizesphysical laws

Fails to capture cumulative interference from (many) far-away transmitters

Sometimes pessimistic decisions and conflicting schedules

21 / 47





SINR Model (Physical Model)

For a given frequency f , the received signal power from sender si to its intendedreceiver ri is:

Pri(si) =

P

d(si, ri)α,

where α ∈ [2, 6] is called the path-loss exponent; value depends on externalconditions.

22 / 47





SINR Model (Physical Model)

For a given frequency f , the received signal power from sender si to its intendedreceiver ri is:

Pri(si) =

P

d(si, ri)α,

where α ∈ [2, 6] is called the path-loss exponent; value depends on externalconditions.

A transmission from sender si to its intended receiver ri is successful if the ratio,SINRri

, of the received signal power to the cumulative interference plus noiseN at ri is more than a hardware-dependent threshold β:

SINRri=

Pd(si,ri)α

Iri+N =

Pd(si,ri)α

∑

j 6=iP

d(sj ,ri)α +N≥ β

22 / 47





Parameters

CC2420 radio parameters with receiver sensitivity −95 dB

Path-loss exponent α = 3.5, transmit power −6 dB

Percentage of Conflicting Schedules:SINR vs. Graph-based Model

100 200 300 400 500 600 700 8000

5

10

15

20

25

30

35

40

Number of Nodes

Con

flict

Lin

ks (

%)


Observations

For a given frequency, the amountof conflict increases as the networkgets denser, reaching almost 40%for densest deployment with asingle frequency

With multiple frequencies, theamount of conflict is much less

23 / 47



Problem Formulation and Approach

Problem Formulation in SINR

Joint Frequency and Time Slot Assignment

Given a connected network of arbitrarily deployed nodes,K orthogonal frequencies, and a routing tree T =(V, ET ) rooted at the sink s ∈ V

Assign a frequency to each receiver in T

Assign a time slot to each edge in T

such that the schedule length is minimized, subject to

SINRri≥ β at every receiver ri Cumulative interference

24 / 47




Approach

Link Diversity

Classify the edges in ET based on their lengths ℓi = d(si, ri). Link diversity isthe number of magnitude of different lengths

g(ET ) = |{m | ∃ ei, ej ∈ ET : ⌊log (ℓi/ℓj)⌋ = m}|

Usually a small constant in practice, but theoretically can be equal to the numberof nodes

25 / 47




Approach

Link Diversity

Classify the edges in ET based on their lengths ℓi = d(si, ri). Link diversity isthe number of magnitude of different lengths

g(ET ) = |{m | ∃ ei, ej ∈ ET : ⌊log (ℓi/ℓj)⌋ = m}|

Usually a small constant in practice, but theoretically can be equal to the numberof nodes

Overall Idea

Normalize (w.l.o.g) the minimum edge length to one

LetE =

{

E0, . . . , Elog(emax)

}

denote the set of non-empty length classes, where Ek is the set of edgesof lengths in

[

2k, 2k+1)

, and emax is the longest edge

Partition the problem into disjoint length classes, and process edges ineach class separately

25 / 47




Approach

For Length Class Ek

Divide the 2-D region into a setCk of square grids of lengthηk = δ · 2k, for some constant δ(will choose δ later)

Frequency Assignment:For each cell in Ck, runFrequencyGreedy on thereceivers

Time Slot Assignment:Four color the cells in Ck

Can we still reuse time slotsacross non-adjacent cells of thesame color? If so, how many?

g1 g1

g1 g1

g2 g2

g2 g2

g3 g3

g3 g3

g4 g4

g4 g4

hk=d.2k

g1 g1g2 g2

g1

g1

g3

g3

g1

e e�f f

u u�v v�

e e�f f

u u�v v�

26 / 47



Approximations in SINR

Approximation Algorithm in SINR

Theorem

For cells of the same color in Ck, we can simultaneously schedule at most oneedge in Ek from every non-adjacent cell that lies on the same frequency, so longas the cell size satisfies:

ηk = δ · 2k, for δ = 4

[

8β · α− 1

α− 2

] 1

α

,

where β ≥ 1 is the SINR threshold, and α > 2 is the path-loss exponent.

27 / 47





Theorem

For cells of the same color in Ck, we can simultaneously schedule at most oneedge in Ek from every non-adjacent cell that lies on the same frequency, so longas the cell size satisfies:

ηk = δ · 2k, for δ = 4

[

8β · α− 1

α− 2

] 1

α

,

where β ≥ 1 is the SINR threshold, and α > 2 is the path-loss exponent.

Proof Sketch

Consider one specific edge ei = (si, ri) ∈ Ek in any cell c ∈ Ck

Received power at ri

Pri(si) =

P

ℓαi

≥ P

2α(k+1), ∵ 2k ≤ ℓi < 2k+1

Show that the cumulative interference Iricaused by concurrent

transmissions from all non-adjacent cells is still within β27 / 47





g1 g1

g1 g1

g2 g2

g2 g2

g3 g3

g3 g3

g4 g4

g4 g4

g1 g1g2 g2

g1

g1

g3

g3

g1

g2

g2

g4

g4

g2

g2

g2

g4

g4

g2

g3 g3g4 g4 g3 g4g4

g3 g3g4 g4 g3 g4g4

g1 g1g2 g2 g1 g2g2

g1 g1g2 g2 g1 g2g2

g1

g1

g3

g3

g1

g3

g3

g1

g1

g1

g1

g3

g3

g1

g3

g3

g1

g1

ei

hk=d.2

k

Consider edge ei = (si, ri) ∈ Ek

28 / 47





g1 g1

g1 g1

g2 g2

g2 g2

g3 g3

g3 g3

g4 g4

g4 g4

g1 g1g2 g2

g1

g1

g3

g3

g1

g2

g2

g4

g4

g2

g2

g2

g4

g4

g2

g3 g3g4 g4 g3 g4g4

g3 g3g4 g4 g3 g4g4

g1 g1g2 g2 g1 g2g2

g1 g1g2 g2 g1 g2g2

g1

g1

g3

g3

g1

g3

g3

g1

g1

g1

g1

g3

g3

g1

g3

g3

g1

g1

ei

ej ej ej

ej ej ej

ejej

hk=d.2

k


At most 8 from layer 1

29 / 47





g1 g1

g1 g1

g2 g2

g2 g2

g3 g3

g3 g3

g4 g4

g4 g4

g1 g1g2 g2

g1

g1

g3

g3

g1

g2

g2

g4

g4

g2

g2

g2

g4

g4

g2

g3 g3g4 g4 g3 g4g4

g3 g3g4 g4 g3 g4g4

g1 g1g2 g2 g1 g2g2

g1 g1g2 g2 g1 g2g2

g1

g1

g3

g3

g1

g3

g3

g1

g1

g1

g1

g3

g3

g1

g3

g3

g1

g1

ei

ej ej ej ej ej

ej ej ej ej ej

ej

ej

ej

ej

ej

ej

ej ej ej

ej ej ej

ejej

hk=d.2

k


At most 8 from layer 1

At most 16 from layer 2, ..., atmost 8q from layer q

Add up all the interferences up tolayer ∞

30 / 47





g1

g1

g2

d.2k-2

k+1ri

rj

si

sj

d.2k

Computing Cumulative Interference Iri

From transmitter sj in a layer 1 non-adjacent cell of the same color

Iri(sj) =

P

ℓαij

≤ P

[2k(δ − 2)]α, ∵ ℓij ≥ δ · 2k − 2k+1

31 / 47





g1

g1

g2

d.2k-2

k+1ri

rj

si

sj

d.2k



Iri(sj) =

P

ℓαij

≤ P

[2k(δ − 2)]α, ∵ ℓij ≥ δ · 2k − 2k+1

In general, ℓij ≥ 2k {(2q − 1)δ − 2} in layer q

31 / 47





g1

g1

g2

d.2k-2

k+1ri

rj

si

sj

d.2k



Iri(sj) =

P

ℓαij

≤ P

[2k(δ − 2)]α, ∵ ℓij ≥ δ · 2k − 2k+1

In general, ℓij ≥ 2k {(2q − 1)δ − 2} in layer q

Adding up

Iri≤

∞∑

q=1

8qP

[2k {(2q − 1)δ − 2}]α =8P

2(k−1)αδα· α− 1

α− 2≤ Pri

(si)

β

31 / 47





Theorem :O(g(ET )) Approximation

Given a routing tree T on an arbitrarily deployed connected network in 2-D, andK orthogonal frequencies, the algorithm gives a O (g(ET )) approximation onthe optimal schedule length.

32 / 47





Theorem :O(g(ET )) Approximation

Given a routing tree T on an arbitrarily deployed connected network in 2-D, andK orthogonal frequencies, the algorithm gives a O (g(ET )) approximation onthe optimal schedule length.

Proof Sketch

Choice of the critical cell c in which the number of edges on the samefrequency Lm∗

c is maximum across all length classes

Show that OPT will take at least Lm∗

c /µ slots, for

µ =

[

2(√

2 · δ + 1)]α

β

Show by contradiction that OPT cannot schedule µ + 1 edges on the samefrequency in any cell

32 / 47





Proof Sketch (cobmining together)

Γ ≤ 4 ·maxk,c{|γc∈Ck

|} · g(ET )

≤ 8 ·maxk,c

{

Lφc∈Ck

}

· g(ET )

≤ 8 ·maxk,c

{(

4

3− 1

3K

)

· Lm∗

c∈Ck

}

· g(ET )

≤ 8µ ·(

4

3− 1

3K

)

· g(ET ) ·OPT

= O (g(ET ))

33 / 47


Throughput-Delay Trade-off

Outline




4 Conclusions

34 / 47



Motivation

Properties of Spanning Trees

0 50 100 150 2000

20

40

60

80

100

120

140

160

180

200

x−axis

y−ax

is

Shortest Path Tree (shallow and fat)

High node degree ⇒ low throughput

Few hops ⇒ low delay

35 / 47



Motivation


0 50 100 150 2000

20

40

60

80

100

120

140

160

180

200

x−axis

y−ax

is

Shortest Path Tree (shallow and fat)

High node degree ⇒ low throughput

Few hops ⇒ low delay

0 50 100 150 2000

20

40

60

80

100

120

140

160

180

200

x−axis

y−ax

is

Minimum Interference Tree (weighted MST)[Mobihoc ’04] (deep and skinny)w(u, v): no. of nodes covered by the union of twodisks centered at u and v, each of radius |uv|

Low node degree ⇒ high throughput

More hops ⇒ high delay

35 / 47



Motivation

Evaluation of AUDG on SPT & MIT

Parameters

Random geometric graph on a region of size 200× 200 with R = 25

Shortest Path Tree

100 200 300 400 500 600 700 8005

10

15

20

25

30

35

40

45

50

Number of Nodes

Sch

edul

e Le

ngth


Minimum Interference Tree

100 200 300 400 500 600 700 8005

10

15

20

25

30

35

40

45

50

Number of Nodes

Sch

edul

e Le

ngth

MIT, K=1MIT, K=3MIT, K=5

36 / 47



Motivation

Tree Property for Bounded Throughput

Theorem

If the maximum node degree of the routing tree is bounded by a constant∆C > 0, then there exists an algorithm that gives a constant factor 8µα · ∆C

approximation on the optimal schedule length, where µα > 0 is a constant for agiven cell size α ≥ 2R and given node deployment.

37 / 47



Motivation

Tree Property for Bounded Throughput

Theorem

If the maximum node degree of the routing tree is bounded by a constant∆C > 0, then there exists an algorithm that gives a constant factor 8µα · ∆C

approximation on the optimal schedule length, where µα > 0 is a constant for agiven cell size α ≥ 2R and given node deployment.

Properties

Degree-bounded spanning trees? Minimum Degree Spanning Tree isNP-hard [SODA’92]

Is constant factor approximation on schedule length and delay achievable?

37 / 47



Bicriteria Formulation


Bounded-Degree Minimum-Radius Spanning Tree

P = (Degree, Radius, Spanning Tree)Radius: R(T ): Maximum hop distance from any node to sink in T∆∗: Budget on max degreeGoal: Find a spanning tree of min radius subject to max degree ∆∗

38 / 47





Bounded-Degree Minimum-Radius Spanning Tree

P = (Degree, Radius, Spanning Tree)Radius: R(T ): Maximum hop distance from any node to sink in T∆∗: Budget on max degreeGoal: Find a spanning tree of min radius subject to max degree ∆∗

Approximation Definition

Algorithm A is an (α, β)-approximation to a bicriteria optimization problem P =(Degree, Radius, Spanning Tree) if:

∆(T ) ≤ α + ∆∗

R(T ) ≤ β ·R∗(T )

where R∗(T ) is the min radius of any spanning tree T whose max degree is ∆∗.

38 / 47



Optimal Spanning Trees

Algorithm Overview

Algorithm ABDMRST

Three phases:

1 Construct a GlobalBackbone Tree of lowradius.

2 Constructdegree-bounded LocalSpanning Trees.

3 Merge the localspanning trees and theglobal backbone tree.

R/2

Completegraph

39 / 47




Algorithm Overview

Global Backbone Tree

r1

r3

w1

r4

r2

s

w2

r5

r6

R

R/2

r7

R

R

r8

r9

r10

40 / 47




Algorithm Overview

Global Backbone Tree

r1

r3

w1

r4

r2

s

w2

r5

r6

R

R/2

r7

R

R

r8

r9

r10

Local Spanning Tree

wk

rj

v1

R/2

40 / 47





0 50 100 150 2000

20

40

60

80

100

120

140

160

180

200

0 50 100 150 2000

20

40

60

80

100

120

140

160

180

200

0 50 100 150 2000

20

40

60

80

100

120

140

160

180

200

Bounded-Degree Minimum-RadiusSpanning Tree, ∆∗ = 4

41 / 47




Approximation Result & Evaluation

Theorem

Algorithm ABDMRST gives a constant factor (α, β) bicriteria approximation forthe Bounded-Degree Minimum-Radius Spanning Tree, where α = 10 and β = 5.

42 / 47




Approximation Result & Evaluation

Theorem

Algorithm ABDMRST gives a constant factor (α, β) bicriteria approximation forthe Bounded-Degree Minimum-Radius Spanning Tree, where α = 10 and β = 5.

Schedule Length

100 200 300 400 500 600 700 8005

10

15

20

25

30

35

40

45

50

Number of Nodes

Sch

edul

e Le

ngth

BDMRSTSPTMIT

Max Delay

100 200 300 400 500 600 700 8000

20

40

60

80

100

120

Number of Nodes

Max

imum

Del

ay (

Tre

e R

adiu

s)

BDMRSTSPTMIT

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Conclusions

Outline




4 Conclusions

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Conclusions

Contributions

Maximizing aggregated convergecast throughput using multi-channelscheduling

Constant factor approximation on UDG∆(T ) · log(n) approximation on DGO(g(ET )) approximation in SINR

Throughput-delay trade-off in the same optimization frameworkBicriteria formulationConstant factor approximation on constructing bounded-degreeminimum-radius spanning trees

Efficient, distributed topology control in 3-DSimple orthographic projection based approach extending 2-D resultsRobust spherical Delaunay triangulation based algorithm

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Conclusions

Publications

Book Chapters

1 O.D. Incel, A. Ghosh, and B. Krishnamachari, Scheduling Algorithms for Tree-Based Data Collection in Wireless Sensor Networks,Theoretical Aspects of Distributed Computing in Sensor Networks, Springer, 2010.

2 A. Ghosh and S.K. Das, Coverage and Connectivity Issues in Wireless Sensor Networks, Mobile, Wireless and Sensor Networks:Technology, Applications and Future Directions, John Wiley & Sons, 2006.

Journal Papers

1 A. Ghosh, O.D. Incel, V.S. Anil Kumar, and B. Krishnamachari, Multi-Channel Scheduling and Spanning Tree Algorithms:Throughput-Delay Trade-off for Fast Convergecast in Sensor Networks, ACM/IEEE Transactions on Networking, Feb 2010 (sub).

2 O.D. Incel, A. Ghosh, B. Krishnamachari, and K. Chintalapudi, Fast Data Collection in Tree-Based Wireless Sensor Networks,IEEE Transactions on Mobile Computing, Dec 2009 (rev).

3 A. Viswanath, P. Dutta, M. Chetlur, P. Gupta, S. Kalyanaraman, and A. Ghosh, Perspectives on Quality of Experience for VideoStreaming over WiMAX, ACM SIGMOBILE Mobile Computing and Communications Review, Oct, 2009.

4 A. Ghosh and S.K. Das, Coverage Connectivity Issues in Wireless Sensor Networks: A Survey, Journal of Pervasive and MobileComputing, 4(3):303-334, June 2008.

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Conclusions

Publications

Conference Papers (reverse chronologically)

1 A. Ghosh, R. Jana, V. Ramaswami, J. Rowland, and N.K. Shankar, Modeling and Characterization of Large-Scale Wi-Fi Traffic inPublic Hot-Spots, IEEE INFOCOM, 2011 (sub).

2 A. Ghosh, O.D. Incel, V.S. Anil Kumar, and B. Krishnamachari, Optimal Spanning Trees for Fast Data Collection in SensorNetworks, IEEE INFOCOM Student Workshop, Mar 2010.

3 A. Ghosh, O.D. Incel, V.S. Anil Kumar, and B. Krishnamachari, Multi-Channel Scheduling Algorithms for Fast AggregatedConvergecast in Sensor Networks, IEEE MASS, October 2009.

4 S.W. Lee, D. Yoon, and A. Ghosh, Intelligent Parking Lot Application using Wireless Sensor Networks, International Symposiumon Collaborative Technologies and Systems (CTS), May 2008.

5 A. Ghosh, L. Pereira, T. Yan, and H. Cao, Modeling Wireless Sensor Network Architectures using AADL, European Congress onEmbedded Real Time Software (ERTS), Jan 2008.

6 A. Ghosh, Y. Wang, and B. Krishnamachari, Efficient Distributed Topology Control in 3 Dimensional Wireless Networks, IEEESECON, Jun 2007.

7 A. Ghosh and S.K. Das, A Distributed Greedy Algorithm for Connected Sensor Cover in Dense Sensor Networks, IEEE/ACMDCOSS, Jul 2005.

8 A. Ghosh, Estimating Coverage Holes and Enhancing Coverage in Mixed Sensor Networks, IEEE LCN, Nov 2004.

9 S.K. Ghosh and A. Ghosh, A Plan-Commit-Prove Protocol for Secure Verification of Traversal Path, IEEE InternationalConference on Networks (ICON), Nov 2004.

Manuscripts

1 T. Fu, A. Ghosh, E.A. Johnson, and B. Krishnamachari, Energy-Efficient Deployment Strategies in Structural Health Monitoringusing Wireless Sensor Networks, Structural Control and Health Monitoring, 2009 (manuscript).

2 A. Ghosh, A.H. Patel, C.R. Sastry, Radio Frequency-Based Localization in Wireless Sensor Networks, Siemens Corporate ResearchTechnical Report, Aug 2009.

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Conclusions

Acknowledgments

Collaborators

USC (EE, Civil): Bhaskar Krishnamachari, Erik Johnson, Yi Wang, Tat Fu

Bogazici University: Ozlem Durmaz Incel

Virginia Tech: Anil Vullikanti

University of Texas: Sajal K. Das

IBM Research: Shivkumar Kalyanaraman, Partha Dutta, Malolan Chetlur

Siemens Corporate Research: Chellury Ram Sastry

Microsoft Research: Krishnakant Chintalapudi

Eaton Corporation: Ting Yan, Luis Pereira, Hui Cao

AT&T Labs Research: Vaidyanathan Ramaswami, Rittwik Jana, N.K.Shankar

Thank You!

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