Minimum Average Routing Path Clustering Problem in Multi-hop 2-D Underwater Sensor Networks...

Minimum Average Routing Path Clustering Problem in Multi-hop

2-D Underwater Sensor Networks

Presented By Donghyun Kim

Data Communication and Data Management Laboratory University of Texas at Dallas

DIMACS/DyDAn Workshop: Approximation Algorithms in Wireless Ad Hoc and Sensor Networks

DIMACS Center - Rutgers April 22 - 24, 2009

AgendaIntroductionPreliminariesMinimum Average Routing Path Clustering

Problem (MARPCP) - approximation schemeFaster 30 - approximation scheme

Presented by Donghyun Kim on April 22, 2009Data Communication and Data Management Laboratory at The University of Texas at DallasDIMACS

)15(

Underwater Sensor Networks (USNs)Applications

◦Oceanographic data collection◦Pollution monitoring◦Offshore exploration◦Disaster prevention◦Assisted navigation◦Tactical surveillance


Underwater Sensor Networks (USNs) – cont’Variable number of sensors and vehicles

◦Static sensors for traditional data collection◦Unmanned Underwater Vehicles (UUV) ◦Deployed to perform collaborative monitoring

tasks over a given areaConnecting underwater instruments by

means of wireless links based on acoustic communication


Underwater SinksMultiple underwater sinks for relaying

data to onshore or surface stationsInvolve in a lot of data transmissionSpend more energy to transmit data to

offshore or surface sinksExpensive





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Routing Schemes in Wireless NetworksDirect routing

◦Simple◦Not cost and energy efficient

Multi-hop routing◦Evade energy exhausting long range direct

communication◦Increases the complexity of the routing ◦In multi-hop routing, the energy consumption

for transmitting a message increases as the number of hops grows


Clustering for USNsUSNs have decent mobilityIn dynamic wireless networks, clustering

ensures basic level system performance (i.e. throughput and delay)

Multi-level hierarchies for scalable ad-hoc routing (E.M. Belding-Royer, Wireless Net-works, 2003)


Clustering-based Routing in Wireless Networks

UW-Sinks

Normal Nodes

Clusterheads


Clustering-based Routing in Wireless Networks – cont’

UW-Sinks

Normal Nodes

Clusterheads


Data Fusion in Wireless Sensor Networks

Normal Nodes

Clusterheads

)12,,( oCdc

)10,,( oCfe

)11,,( oCba

It is around 10-12


AgendaIntroductionPreliminariesMinimum Average Routing Path Clus-

tering Problem (MARPCP) - approximation schemeFaster 30 - approximation scheme


)15(

GOAL

Finding an energy efficient clustering scheme for USNs using clustering-based routing scheme and limited data fusion (or requiring some level of data precision).


AssumptionsUSNs are homogeneousEach clusterhead is used as a local data

aggregation pointClustering-based shortest path routing is

used as a routing scheme


Problem Formulation

d

s

2),(0

1),(0

),()(),(),(),(

dCHHopdist

CHsHopdist

dCHHopdistpwCHsHopdistdsRoutedist

s

s

sCHCHMWPp

s

ds

cjkjmk

cjkjmk

UCHRoutedistn

cnUCHRoutedist

11

11

)1),((min

),(min

The number of hops in total routing path


Problem Formulation – cont’Minimum Average Routing Path Clustering

Problem (MARPCP)◦Given a set of sensor nodes and UW-Sinks on the

Euclidean plane, MARPCP is find a set of cluster-heads such that each sensor node is adjacent to at least one clusterhead, and the average distances from each clusterhead to its nearest UW-Sink is minimized. In other words, we want to minimize

1),(,,such that

/))1),((min(1

1

ji

cjkjmk

CHsHopdistji

nUCHRoutedist


A relaxation from MARPCP to Minimum Weight Dominating Set Problem (MWDSP)

3

2

1

1

1

1

1

3

2

3

2

3

4

1





)15(

Algorithm 1Lemma 1

◦For any clusterhead and a UW-Wink , . )1),((31),( UCHHopdistUCHRoutedist

CH U

U

CH

1CH

2CH

3CH

1v

2v

3v

UvCHvvCHvvCHvCH

lCH,U)Routepath(

lll

222111

)1(3Length: Feasible

)1(Length:),( 21 lUvvvCHUCHMinpath l


Algorithm 1 – cont’Corollary 1

◦Let A and B be a MARPCP and its corresponding (relaxed) MWDSP instances, respectively. Denote the cost function of feasible solutions for MARPCP and MWDSP by and , respectively. Then, for any feasible solution , .

Proof of Corollary 1◦By Lemma 1, for every ,

)(Aw )(BwF

)(3)( FwFw BA

Fv )1),((31),( UvwUvw BA

)(3)1),((3)1),(()( FwUvwUvwFw BFv

BFv

AA


Algorithm 1 – cont’Theorem 1

◦A -approximation algorithm for MWDSP is a 3 -approximation algorithm for MARPCP.

Proof 1◦ ◦ ◦

)()( ABBB OPTwOPTw )()( AAAB OPTwOPTw

)()( AABB OPTwOPTw

)(3)( FwFw BA )(3)(3)(3)( AABBBA OPTcwOPTcwFcwFw

cc


UW-Sinks

Normal Nodes

Clusterheads

Algorithm 1 – cont’Existing algorithms for MWDSP.

◦Slow algorithms (centralized, enumeration) 72-approximation = 216-app. for MTRPCP -approximation = -app. for MTRPCP

◦Quick Algorithm (distributed, greedy) -approximation = -app. For MTRPCP

)5(

)log(n

)15(

)log(n


A Faster Heuristic Algorithm for MARPCP with A Constant Performance Ratio

Presented by Donghyun Kim on April 22, 2009Data Communication and Data Management Laboratory at The University of Texas at Dallas

2

DIMACS




)15(

Algorithm 2 AnalysisLemma 2

◦Let is an MIS included in of a node . Then, .

M )(vN v

5|| M


: all node in Level in tree

Algorithm 2 Analysis – cont’Theorem 2

◦ Algorithm 2 is a 30-approximation algorithm for MARPCP.Proof of Theorem 2

jU

)},,,,{( 21 EsssSUG njj

1 level

2 level l

3 level

jjj UGT at rooted in path treeshortest a :


1G

2G3G

3U

1U

2U

jG

DIMACS

),( jiL i jT

Algorithm 2 Analysis – cont’◦Consider ◦All nodes in is dominated by◦Let be the subset of dominated by

. Then, ◦As is dominated by , from

lemma 2, we have

jBB GOPTOPTj

j

mj MISD 1

BOPT),,( kjiM

),,(111 kjimk

li

mj MD j

kMIS

),,(1 kjimk M ),( jiB LOPT

j

||5|| ),(),,(1 jiBkjimk LOPTM

j


),( jiB LOPTj

Algorithm 2 Analysis – cont’◦By Algorithm 1, each must lie in either level

of its corresponding shortest path tree. Thus,

since . If follows that

◦Summing up for and we obtain


),,( kjiM1or ,,1 iii

ii 21

jli1mj 1

DIMACS

Future WorkDesign a quick approximation algorithm

◦Ratio should be better than 30.Design a generalized distributed approxi-

mation algorithm◦Support trade-off between data accuracy and

energy-efficiencyHow to cluster USNs to deal with the

unique properties and challengesHow to incorporate an energy model?


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