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Efficient Integration of Multi-hop Wireless and Wired Networks with QoS Constraints Bell Laboratories, Lucent Technologies, 600 Mountain Avenue, Murray Hill, NJ 07974 ABSTRACT 1. INTRODUCTION Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Mobicom 2002, September 23-28, 2002, Atlanta, Georgia, USA.. Copyright 2002 ACM 1-58113-486-X/02/0009 ... 5.00.

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Efficient Integration of Multi-hop Wireless and WiredNetworks with QoS Constraints

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Bell Laboratories, Lucent Technologies,

600 Mountain Avenue, Murray Hill, NJ 07974

ABSTRACT��������� �"!$#&%'�)(��*�,+�-.!$��/$�0-213!$�)4�5,-.67�"8�+3-'�*��9)(0��(�9;:"(<->=?%'��-'(@/:A(B+C5,�D��EF%'�"�G/��,(38H!I:A�G/*!$J0%./$J3!$-K8L�"!�%.�)(0(�-'%./$��(09��G/I:A/$��%K6MJ05N/$�NEO���)1�P�N!$-'5�-'�*�Q(0->/R���A!$#S���P��/$���P�N!$-D+�40:"%I#34T�"(0-)US�P���,5�-V-.(0�*J�!$��(�9?WX�@Y!$-'ZSJ��N!$-'6?-'(@/$� �*J�%>��:"� 4B:"(0+3�P�,+3/$��:A(B+�+�-'5,:'[@\������,� �,(38H!I:A�G/*!$J0%.E/$J3!$-P�,�]J0�*-.8HJ0538L�"!�+�-'�*��9"(0��(09�5��D�<%'�"�G/�:"(0+^8_:A�G/�+�-.105��D[@-D+K:A%'%'-'�*�(�-./R� �"!$#S�X��(2!$J3!I:"5`:A(B+2�*J04�J�!$40:"(a:�!$-D:"�'\cbO/c6�:'[2:A5,�*��4T-�J0�*-D+8H�"!c1�!$��dS�,+���(09^:"%'%'-.�*�Q/$�K�*-.(0�*�"!Q(�-./R� �"!$#S�P�"!P8L�A!c->=?%'��-'(@/P8_:"%.�,5NE�N/O[e1�5f:A%'-'6?-'(@/P��(2�P�N!$-'5�-'�*�X(�-./R� �"!$#S�'\]bR(�/$��-'�*-�(0-./O���A!$#3�P�*�"6?-(��S+�-'�c:A!$-�%I�0�"�*-'(a:"�c:"%.%'-'�*�Q1T�)��(@/$�X:A(B+�8HJ0(�%./$���)(g:"�Q9h:�/$-.��:'[3�/$�i:A%'%'-'�*��:V�P�N!$-D+?4B:A%>#S4T�"(0-)\�j�:"%I��:"%.%'-'�*��1T�"�,(@/]�*-.!$dh-'� :k%'5�J0�GE/$->!X�A8`�N/$�c(�-D:A!$4@[�J0�*-.!c:"(0+2:^�*10:"(0(���(09^/*!$-'-k!$�@�A/$-D+a:A/P/$�0-�:A%.E%.-'�*�c1T�"��(S/Q���PJ0�*-D+�8L�"!Q6?-'�*�$:A9)-i+�-.5,��dh->!*[@\����0-V���A!$#e:"+0+S!$-'�*�*-'�4T�A/$�l/$�0-K+�-'�*��9)(l�)1�/$��6?��mD:�/$�,�"(&:"(0+C/$�0-?�"1T-.!I:A/$���"(;:"�*1T-'%>/$�M�A8/$��-^�G[3�G/$-'62\�n3!$�)6o/$��-^+3-'�*��9)(C1T-.!$�*1T-'%./$��dh-"Up� -K1�!$-.�*-'(@/V1T�)5N[SE(��)6?�,:"5`/$��6?-?:A101�!$�Dq3��6�:A/$���)(r:"5�9"�"!$�N/$�06?�k8L�A!i1B:A!*/$�N/$���)(���(09e/$��-(�-./R� �"!$#M(0�S+�-.�]��(@/$�k6?��(0��6�:"53(SJ06^4T->!��"8s+����LtG�"��(S/]%'5�J0�G/$->!$�]/$�B:�/�$:�/$���G8H[;6MJ05N/$��105�-K%'�"(0�G/*!I:"��(@/$�'u j]:A%>��%.5,J��G/$-.!M�,��!$-DZ@J0�N!$-D+C/$�a4T-:�%'�"(0(0-.%./$-D+a9"!I:A10�g�P��/$�C:A(rJ�101T-.!c4T�)J�(B+a�)(g�N/$�X!I:)+3��J0�'\Vvl-:A�*�*J06?-X/$�0:A/P-D:A%>��(0�S+3-V�B:A�c:���-'��9"�S/iwL!$-'13!$-'�*-'(@/$��(09M��/$�P40:"(B+SE�P�,+S/$��!$-'ZSJ��N!$-'6?-'(@/>x�:A(B+K/$�0-�/$�A/I:"5B��-.�,9"�@/��"8y:"5�5T%'5�J0�G/$->!�(0�S+3-'�����:"5��*�;4T�)J�(B+3-D+p\z�[{43!$-D:"#S��(09l/$��-21�!$�"405�-'67��(@/$�l/R� ���*J043E13!$�)4�5,-.6?�P:"(B+��*�)5�dS��(09K-':"%I�e�)(�-V�*-'10:A!I:A/$-.5�[@US� -k1�!$�)1T�"�*-V1T�)5N[SE(��)6?�,:"5�/$��6?-?:"1�1�!$�Dq3��6�:A/$���)(r:"5�9)�A!$�N/$�06?��/$�B:A/�%':"5�%'J05,:�/$-��*�"5�J�E/$���"(0�K�P�N/$�0��(|:r%'�"(0�G/I:"(@/K8L:"%./$�A!��"8c/$�0-e�"1�/$��6�:"5��"(0-'�'\{n�!$�"6/$��-��)1T-.!I:�/$�,�"(adS�,->�P1T�)��(@/DUB��-���(@/*!$�S+�J0%.-M:A(g:)+�:"1�/$��dh-�+3-'5���dh-.!*[6?-.%>�0:"(0���*6}/$�0:A/�6�:Aq3��6?��m'-'�V/$��-K/$��!$�)J�9)��10J�/��A8�-D:A%>��%.5,J��G/$-.!�P�N/$���)J�/QdS���)5,:A/$��(�9K/$�0-�WX�hY�%'�)(��G/*!I:"��(@/$�'\~��3�p�i�B�A���)��v��N!$-'5�-'�*�r�c%.%'-'�*�g�X-./O���A!$#�U^YS-'(0�*�A!g�X-./O���"!$#S�'U�c(0�N/P�V���*#e�c!I:"10���'UT� 5�J��G/$-.!$��(09�UB�c1�1�!$�Dq3�,6�:�/$���)(��c5�9)�A!$��/$��6?�'\

1. INTRODUCTION����-Q/*!$-.6?-'(B+3�)J0�]:)+3d):A(0%'-P�A8s�P�N!$-'5�-'�*��%'�"6?6^J�(0��%D:A/$���"(K/$-'%>�3E(��)5��)9"��-'�X�0:"�P1�!$�"6?1�/$-D+�/$�0-k+3-'dh-'5��)1�6?-'(@/��"8�(�-.��P�N!$-'5�-'�*�V:A1�E1�5��,%':A/$���)(��'\��Q6?�)(09&/$�0-.�*-;(0-.��:A10105���%D:�/$�,�"(0�g��-�8H�)J0(0+�/$��-43!$�h:"+�4B:A(B+?�P�N!$-'5�-'�*�X:A%'%'-'�*��w�z]vC�Xx]�G[3�G/$-'6?�V�N�.�y:"(0+�/$��-c�P�N!$-.E5�-'�*���*-'(��*�"!�(�-./R� �"!$#S�a� �SU�����\�z]vC���G[��G/$-.6?�K1�!$��dS�,+�-e43!$�h:"+3E40:"(0+�:"%'%.-'�*�C8H�"!C!$-'�*�,+�-'(@/$�,:"5M%'J0�G/$�"6?-.!$�a8L�A!l4T�A/$��/$-'5�-'10���)(�-

Permission to make digital or hard copies of all or part of this work forpersonal or classroom use is granted without fee provided that copies arenot made or distributed for profit or commercial advantage and that copiesbear this notice and the full citation on the first page. To copy otherwise, torepublish, to post on servers or to redistribute to lists, requires prior specificpermission and/or a fee.Mobicom 2002, September 23-28, 2002, Atlanta, Georgia, USA..Copyright 2002 ACM 1-58113-486-X/02/0009 ... � 5.00.

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(b) The optimal partition to multiple-hop clusters with radius at most 5.

- A cluster. - A cluster-head/

access-point.

(c) The optimal partition to multiple-hop clusters with radius at most 5 and weight at most 10.

(a) The optimal partition to single-hop clusters with radius R=1.

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�G/*!$J0%>/]/O����6?-'%I�B:"(����*6?�'À�w_�fx��Q(?-.=?%'��-'(@/]%'5�J0�G/$-.!$��(�9M:A5�9)�"!$�N/$��6/$�B:�/^13!$�S+�J�%'-'�M:g�*6�:A5�5�(SJ06^4T->!��"8c+�-'5���dh-.!*[r/*!$-'-'�i/$�B:A/M%'��dh-.!:"5�5`/$�0-M(0�S+3-'��:"(0+g�$:�/$���G8H[C/$�0-^9"��dh-'(lWX�@Ya%'�)(��G/*!I:"��(@/$�'\ew_���fxX�+�-.5,��dh->!*[^6?-'%I�B:A(0���*6·:A/]-D:A%>�?%'5�J��G/$-.!]/$�0:A/]6�:Aq3��6?��m'-'��/$�0-P%'5�J��GE/$-.!M/$��!$�)J�9)��10J�/��P�N/$�0�"J�/^d3���"5f:�/$��(09g/$�0-eWX�@Yl%'�"(0�G/*!I:"��(@/$�?:A(B+�P�N/$��-.=?%'��-'(@/�%I�B:"(�(0-'5QJ�/$��5���mD:A/$���"(s\°bO({/$�0-2!$-'�G/��"8k/$�������*-.%.E/$���)(pUB��-M+�-'�*%>!$�,4T-�/$�0-i+3-'5��,d)-.!*[e6?-.%>�0:"(0���*62\P�������V+�-.�*%.!$��1�/$���)(���P-'�*�*-'(@/$�,:"5�8L�"!QJ�(B+�->!$�G/I:"(B+3��(09M/$��-V%'�"(0�G/*!I:"��(@/$�P�"8�/$��-V%'5�J0�G/$->!*E��(09�:A5,9"�"!$�N/$�062U0-)\ 9�\�UB/$��-V6�:Aq3��6�:"5�!I:)+3�,J��P�"8�:K%'5�J0�G/$->!DUTÁM\]n0�A!�*��6?105���%'�N/R[@U���-e:"�*�*J06?-�/$�B:�/K/$�0-�J01��G/*!$-D:"6 :"(0+|+3���P(��G/*!$-D:"64B:A(B+S�P�f+S/$��!$-DZ@J���!$-.6?-'(@/$���"8�-'d)-.!*[�(0�S+�-V:A!$-k/$�0-V�$:A6?-)\

3.2 The Delivery Mechanism� �)(��*�,+�-.!^:2%'5�J0�G/$-.!Kù»úÄêä�P�N/$�&:a+�-'5���dh-.!*[C/*!$-'-,�iwFùXë$ìWLx!$�@�"/$-'+�:A/i:A(;:"%'%.-'�*��1T�)��(@/�ý�î|ùä:A(B+C:"�*�*J�6?-K/$�B:A/k/$��-M/*!$-'-+�-.1�/$�2���VÁi\QY3��(0%.-)U�:"5�5�6?-.�*�$:"9)-.�c/*!I:Ddh-.!$�*-�/$��!$�"J09)��/$�0-i:"%'%.-'�*�1T�)��(@/DUS/$�0-X/$�3!$�)J�9)�01�J�/��A8�/$�0-c%'5�J0�G/$-.!Q���P6�:Aq3��6?��m'-D+K�P�0-'(�/$�0-:"%.%'-'�*�^1T�"��(S/M���M4�J0�G[l:"5�5 /$��-�/$��6?-K�P�N/$�;-.=?%.�,-.(S/^+0:�/I:e/*!I:"(��GE6?���*�*���)(s\r�����,�M9)�):"5����^�"4�/I:"��(�-D+;4S[r-'6?1�5,�D[3��(09a%'�"5�5,���*���)(�8H!$-'-T.����-��)1�/$��6�:A5y�*�)5�J3/$�,�"(0�P��-.!$-k8H�)J0(0+e4@[e%I�0-.%>#S��(09?:A5�5s/$�0-�1T�"�GE�*��40��5��N/$�,-.�'\

a

b

c

d

e

f

g

h

i

j k

l

level 1

level 2

level 3

level 4

y - access point m(t 0 ,i)

m(t 0 -2,c )

m(t 0 -4,i )

m(t 0 -6,d )

m(t,v) - a message originated at time t and designated to node v.

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y - access point a b c d

1 2 3 4 5 6 7 8 9

10

12 13 14 15 16 17 18 19

11

d

d

d

d

d, 0

d, 0

d, 0

d, 0

d

d

d

d

d, 0

d, 0

d, 0

d, 0

c, 4

c, 4

c, 4

c,4

c, 4

c, 4

c

c

c

c

c

c

d

d

d

d

d, 0

d, 0

d, 0

d, 0

c, 4

c, 4

c, 4

c

22 23 24 25 26 27 28 29

21 20

30

d, 0

d, 0

d, 0 c, 4

V, 7 The

message direction

The source or destination node

The reserved slot for

upstream data

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5.1 Coverage with Bounded Radius Clusters� �"(0�*�,+�->!^:�J0(0�N/i+3�,�*#g9A!I:"10�;é^wFê�ë$ìixV:"�i+�-.�*%.!$��4T-D+l��(;YS-'%.E/$���"(^�@\����0-Q®$©"­" >¬ ¥D   ¥)¦  ©A¬>�L§HÒ@³|5��@�"#3�s8L�"!y/$�0-�6?��(0��6�:"5"(3J�6^4T-.!�A8Q%'5�J0�G/$-.!*EF�0-':)+��i�*J0%I�l/$�0:A/i/$�0-'�N!^ÁcEF(0-'��9)�S4T�A!$�0�@�S+��i%'��dh-.!^:"5�5/$��-e(��S+�-'�'\<���0���?���K/$�0-e�$:A6?-a:"�?5��@�"#3��(�9r8L�A!�/$�0-e6?��(��,6MJ06+3�)6?��(B:�/$��(09?�*-./c�"8�/$�0-�1T�D��->!V9"!I:A10�CéÙ wFê�ë*ì�Ù`x>\PbO(e/$�0���c�*-'%.E/$���"(���-�%'�)(��*�f+3-.!i/$��!$-'-�%'��dh-.!I:A9)-�:"5�9"�"!$�N/$�06?�i/$�B:A/i9"JB:A!I:A(@/$-'-+3�NÐ�-.!$-'(@/Q:"1�1�!$�Dq3�,6�:�/$���)(e!I:�/$�,�"�'\����-k¢0!$�G/X:"1013!$�h:A%>�a-'6?1�5���[3��/$�0-k9A!$-'-D+S[2�*-./c%'��dh-.!MwFY0��xP:"5NE

9"�"!$�N/$�06��"8c� �Sd":A/I:A5X� �S�>�Q:"(B+r��/M���M/$-.!$6?-'+l:  ¬$ $ *ç"¨C«:�·®$©"­�ü >¬ ¥D   ¥)¦  ©"¬I�L§HÒS³^\k���0���V���k:"(g�N/$-.!I:�/$�,d)-K:"5�9"�"!$�N/$�06»/$�0:A/X�*-'5�-'%./$�:�/�-D:"%I�l�N/$-.!I:�/$���)(r/$��-K(0�S+3-M�P���)�*-�ÁcEF(0-.�,9"�S4T�"!$�0�@�S+g%'�"(S/I:A��(0�/$��-e6�:�q���6�:A5 (SJ06M4T-.!^�A8VJ�(0%'��dh-.!$-'+&(��S+�-'�'\��������?:"5�9)�A!$�N/$�06

F 1

F 2

F 3

Strips composed of 3 basic bands.

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(a) Dividing the graph area into squares with width D=2LR=10.

III

D = 2 L R = 10

II

R = 5

R = 5 R = 5

R = 5

I a

b

c

d

(b) The optimal selection of cluster heads at each square.

b c

d a

a b

c

d

(c) The calculated graph partition.

A cluster boundary. A square boundary.

The boundary of an extended square .

A node inside a considered square.

A cluster head node.

A node included only in the extended square.

D = 2 L R = 10

I II III

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(b) Second iteration, selecting a node with n v = 16

- A cluster-head.

28 30 17

8

8

8 11

31

28 22

18 18

19 15

12 15

12 9

18

17

16

14

11

11

15

18

21 15

12 9

13 16 17

7

10

16

13

10

7

16

14

12

9

15 12

9

13 16 16

7

10

16

13

10

7

(a) First iteration, selecting a node with n v = 31

- Uncovered node.

- Covered node.

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(2,c) (2,d)

(3,c) (3,d)

b

c

d

a

a b c

(4,c) (4,d)

(1,c) (1,d)

(2,c) (4,d)

(1,c) (3,d)

(0,c) (2,d)

(5,a)

(1,d) (3,c)

(0,d) (2,c)

(3,d) (5,c)

(2,d) (4,c)

(1,d) (3,c)

(4,d)

d

(2,d) (4,c)

(3,d) (5,b) (5,c)

(4,b) (4,d)

(3,b) (5,d)

(1,b) (4,a)

(2,b) (5,a)

(0,b) (3,a) (3,b)

(4,a) (4,b) (5,a)

(2,b) (3,a)

(1,b )

(2,a )

(2,a) (3,b)

(0,b) (3,a)

(4,4) (5,b)

(0,a) (3,b)

(5,a) (1,a) (4,b)

(2,a) (5,b)

(1,a) (2,b)

b

c

d

a

a

b

c

d

(a) The set of cluster-heads in each 5-neighborhood.

(b) The partitioning to disjoint clusters with radius at most 5.

(3,c) (5,d)

(5,c) (5,d)

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80

100

120

140

160

180

200

220

240

1 2 3 4 5 6

The depth requirement R

The

num

ber

of c

lust

ers

Gready DIS Alg (W=10). Gready SC Alg (W=10) Improved Shift Alg (W=10) Gready DIS Alg (W=20). Gready SC Alg (W=20) Improved Shift Alg (W=20)

ÓPÔHÕBÖy����×�X��lØ s)��ÜCÝ�Û0�AÔL�'�TÙ Ü �Sà>�i�S�3ÙºàDây�|��ÔA<]�S����Ù�à2Û0ÞIHÕ0�B�AÔHàDâ`Ül�?�?ÔfàDâ<�M�3ÔHÕBâpà�s)�TÙ��'à'��Û0ÔLÙpà�ï ÿ��'É�ÛBÙy�<�)ÉSã

20

40

60

80

100

120

140

160

180

200

220

240

260

1 2 3 4 5 6 7 8 9 10

The depth requirement R

Num

ber

of c

lust

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W = 10 W = 15 W = 20 W = 30 W = 40 W = 55 W = 70 W = 100

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8. CONCLUSIONS AND FUTURE WORK��������� �"!$#�1�!$-.�*-'(@/$��:"(^->=?%'��-'(@/�:"(0+M5��D��EO%.�)�G/���(�8H!I:A�G/*!$J0%./$J3!$-8H�"!P%'�"(0(�-'%./$��(09M�G/I:A/$��%V6^J�5N/$��EF���)1K�P�N!$-'5�-'�*�P(0-./O���A!$#3�]�P��/$��¢0q3-D+40:"%I#S4T�)(0-^(0-./O���"!$#T\K���0���k��(�8H!I:A�G/*!$J0%./$J3!$-?%D:"(r4T-KJ0�*-'+g8H�"!�!$-.E+3J0%'��(�9C/$��-�%'�"�G/?�"8Vz]vC�ä�G[��G/$-.6?�K:"(0+�8L�"!�:A%'%'-'�*�*��(�9l�*-'(��*�"!

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9. ACKNOWLEDGEMENTb����"J05,+a5��,#)-i/$�?/$�B:A(0#�z J05�-'(@/ED -'(�-.!Q8L�"!XJ0�*-.8HJ05`+3���*%'J0�*�*���)(��:"(0+r/$�gj`!I:"(��V:"4�4T-.!DU�Êc:�tR-'-'dlÊc:"�G/$�"9)��:A(B+;È2:�!$#;YS6?��/$�C8L�A!/$�0-.��!Q��-'5�1�8LJ�5s%.�)6?6?-'(@/$�'\

10. REFERENCESF GIHKJ*LNMPOCQSR�TVUCW'X�Y[ZEL]\NL]^`_�a[QSb�_dc�Y]eKLgfKLNhiLNJ._�b(X�YNj�LNk._�lN_�b._�m]no L o L]pqaqL]rCs�X tgW'nuMPb(O%_�n]lN_�m[n o XSb(W�QSW�T(TvZwR�R�W�T(TyxPh?z(_dz(W�O�{z(|]W�Z.bVz'Y~}P|N_�QSQSW�m]�CW�T3_�m[n�{Aa[z(a[b(W��wXSbVW'RIzVXSOCm]T(r]LN�v���'���������`�� �C�E�������d�%�y�'�A�~�'Y]f`OCQ�LN�C�[Y~k�O]LqGCYN\%_�m?aN_�bV���C�C�[GCL

F �dH�EL]ZwT(_�nN_[Y~��L]�wOCm]�]YN��L~h~L]p XSmqY[s�LNk.WI¡�l~W�b(�]Yi�EL[^¢O�z�zVXSW%Yo L~\]L]e�_�XST(W�byY[_�m]n�J�L~£ELN��_�bVRI�?L[r o XSbVW�QSW'TVTv¤2m?zVW��Cb�_dzVW'nk.WIz2¡�OCb(U�hgW�m]TVOCb(T'x`pqOy¡�^�Oy¡�W�bwh?�gTVzVW'¥�TvOCm�_�}P|]XS¦]r]Y~�����y�d���V§�v¨[���I©g���C�«ª¬�C­ �A®�ªi¯2�C¯2� � �A���y¨g�A¯&° � �C�y§I�y���y�~�(�yYqG'�C�C±[L

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