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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
Presented by Donghyun Kim on April 22, 2009Data Communication and Data Management Laboratory at The University of Texas at DallasDIMACS
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
Presented by Donghyun Kim on April 22, 2009Data Communication and Data Management Laboratory at The University of Texas at DallasDIMACS
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
Presented by Donghyun Kim on April 22, 2009Data Communication and Data Management Laboratory at The University of Texas at DallasDIMACS
Presented by Donghyun Kim on April 22, 2009Data Communication and Data Management Laboratory at The University of Texas at DallasDIMACS
Presented by Donghyun Kim on April 22, 2009Data Communication and Data Management Laboratory at The University of Texas at DallasDIMACS
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(
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
Presented by Donghyun Kim on April 22, 2009Data Communication and Data Management Laboratory at The University of Texas at DallasDIMACS
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)
Presented by Donghyun Kim on April 22, 2009Data Communication and Data Management Laboratory at The University of Texas at DallasDIMACS
Clustering-based Routing in Wireless Networks
UW-Sinks
Normal Nodes
Clusterheads
Presented by Donghyun Kim on April 22, 2009Data Communication and Data Management Laboratory at The University of Texas at DallasDIMACS
Clustering-based Routing in Wireless Networks – cont’
UW-Sinks
Normal Nodes
Clusterheads
Presented by Donghyun Kim on April 22, 2009Data Communication and Data Management Laboratory at The University of Texas at DallasDIMACS
Data Fusion in Wireless Sensor Networks
Normal Nodes
Clusterheads
)12,,( oCdc
)10,,( oCfe
)11,,( oCba
It is around 10-12
Presented by Donghyun Kim on April 22, 2009Data Communication and Data Management Laboratory at The University of Texas at DallasDIMACS
AgendaIntroductionPreliminariesMinimum Average Routing Path Clus-
tering 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(
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).
Presented by Donghyun Kim on April 22, 2009Data Communication and Data Management Laboratory at The University of Texas at DallasDIMACS
AssumptionsUSNs are homogeneousEach clusterhead is used as a local data
aggregation pointClustering-based shortest path routing is
used as a routing scheme
Presented by Donghyun Kim on April 22, 2009Data Communication and Data Management Laboratory at The University of Texas at DallasDIMACS
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
Presented by Donghyun Kim on April 22, 2009Data Communication and Data Management Laboratory at The University of Texas at DallasDIMACS
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
Presented by Donghyun Kim on April 22, 2009Data Communication and Data Management Laboratory at The University of Texas at DallasDIMACS
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
Presented by Donghyun Kim on April 22, 2009Data Communication and Data Management Laboratory at The University of Texas at DallasDIMACS
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(
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
Presented by Donghyun Kim on April 22, 2009Data Communication and Data Management Laboratory at The University of Texas at DallasDIMACS
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
Presented by Donghyun Kim on April 22, 2009Data Communication and Data Management Laboratory at The University of Texas at DallasDIMACS
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
Presented by Donghyun Kim on April 22, 2009Data Communication and Data Management Laboratory at The University of Texas at DallasDIMACS
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
Presented by Donghyun Kim on April 22, 2009Data Communication and Data Management Laboratory at The University of Texas at DallasDIMACS
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
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(
Algorithm 2 AnalysisLemma 2
◦Let is an MIS included in of a node . Then, .
M )(vN v
5|| M
Presented by Donghyun Kim on April 22, 2009Data Communication and Data Management Laboratory at The University of Texas at DallasDIMACS
: 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 :
Presented by Donghyun Kim on April 22, 2009Data Communication and Data Management Laboratory at The University of Texas at Dallas
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
Presented by Donghyun Kim on April 22, 2009Data Communication and Data Management Laboratory at The University of Texas at DallasDIMACS
),( 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
Presented by Donghyun Kim on April 22, 2009Data Communication and Data Management Laboratory at The University of Texas at Dallas
),,( 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?
Presented by Donghyun Kim on April 22, 2009Data Communication and Data Management Laboratory at The University of Texas at DallasDIMACS