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Computing 2-Hop Neighborhoods in Ad Hoc Wireless Networks 183If both y i and y j exist, x i and y i are on different sides of vz, and x j andy j are also on different sides of vz, then we obtain a contradiction as follow.Assuming i.Any node receiving such a message evaluates whether it has neighbors in therigid piece, and if yes the node computes the set of its neighbors from the rigidpiece which are adjacent to v, based on their coordinates with respect to therigid piece.If v has three or more neighbors in common with a rigid piece, but theyare coliniar, v cannot exactly compute its coordinates with respect to therigid piece, but has exactly two possible value for its coordinates. Then v asksits neighbors in MIS to announce both positions with a packet containing
184 G. Calinescu< nodeID, pieceID, coordinates 1 , coordinates 2 , counter >. Any node y receivingsuch a message evaluates if it has neighbors in the rigid piece, and if yes, asabove, it can compute two sets S 1 and S 2 of nodes in the rigid piece which couldbe the common neighbors with v - assuming v has coordinates coordinates 1 orcoordinates 2 with respect to the rigid piece. At least one of S 1 and S 2 is a setof colinear points, and if both are, they coincide. That set of colinear points isthe set of neighbors common to y and v in the rigid piece.All cases are taken care of and we conclude:Theorem 3. There is a distributed algorithm which, under the assumption thatevery node can estimate the distance to every adjacent node, computes for everynode v the set of its 2-hop neighbors N 2 (v) and the links in between N 1 (v) andN 2 (v) with a total of O(n) messages each of size O(log n) bits.5 Updating the 2-Hop NeighborhoodsIn this section we discuss the message complexity of updating the 2-hop neighborhoodsdue to changes in network topology. We do not address updating thevirtual backbone as this was done in [2]. The proposed protocol is straightforwardand does not use the virtual backbone. We assume geographical knowledgeis available in this section.Before leaving the network, a node u uses its knowledge to let its 2-hopneighborhs know the fact it is leaving as described below. First the node ucomputes a maximal independent set (MIS) in the graph induced by its 2-hopneighborhs. Then u computes at most one “connector” node for each MIS node.As before, MIS is a dominating set, and using an area argument, has constantsize. Node u prepares an < ID, position, leaving, relay > message, with its ownID and position, the fact that it is leaving the network, and the full list of relaynodes. Each node, after receiving such a message, make a note that u is leavingand updates its 2-hop neighborhood accordingly, and, if it finds itself in the listof relay nodes, rebroadcast the message once.When a node v joins the network, it will broadcasts its ID and position.Every existing node which receives this message will rebroadcast the ID andposition of v. Every node y receiving such a message, will update its stored 2-hopneighborhood to reflect the presence of v. Ify is adjacent to v, it will broadcastits ID and position. If y is a 2-hop neighbor of v, it selects a common neighborx and asks x to relay to v the position and ID of y. The total bit complexity ofmessage is O(q log n), where q is the size of the 2-hop neighborhood of v, and itcannot be improved by more than a constant factor since v must find out theIDs of the nodes in its 2-hop neighborhood.6 ConclusionsThe virtual backbone of Alzoubi, Wan, and Frieder [2,21] can be constructedwithout any geographical knowledge: their algorithm “operates” directly on the
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Lecture Notes in Computer Science 2
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Samuel Pierre Michel BarbeauEvangel
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PrefaceAd Hoc Networks are wireless
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Program CommitteeG. Alonso, ETHZ, S
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XTable of ContentsResisting Malicio
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2 H. Dubois-Ferrière, M. Grossglau
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10 H. Dubois-Ferrière, M. Grossgla
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SAFAR: An Adaptive Bandwidth-Effici
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14 J. Doshi and P. Kilambiour proto
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16 J. Doshi and P. Kilambipacket th
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18 J. Doshi and P. Kilambibandwidth
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20 J. Doshi and P. Kilambi5 Simulat
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22 J. Doshi and P. Kilambiquery its
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24 J. Doshi and P. Kilambi4. David
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26 P. Narayan and V.R. SyrotiukThe
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28 P. Narayan and V.R. Syrotiuk2.2
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30 P. Narayan and V.R. Syrotiukrand
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32 P. Narayan and V.R. Syrotiukenti
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34 P. Narayan and V.R. SyrotiukDSRA
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36 P. Narayan and V.R. Syrotiuk7. A
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38 L. Qin and T. Kunzthese two prot
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40 L. Qin and T. Kunzsidered broken
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42 L. Qin and T. KunzP = Prdlog( )
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46 L. Qin and T. KunzFig. 5. Averag
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48 L. Qin and T. Kunz6. J. Broch et
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50 M. Diha and S. Pierrethe propose
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52 M. Diha and S. Pierre3. All proc
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54 M. Diha and S. Pierre3.3 Perform
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56 M. Diha and S. PierreCmip/Cprop0
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58 M. Diha and S. PierreThe tunneli
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Proactive QoS Routing in Ad Hoc Net
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62 Y. Ge, T. Kunz, and L. LamontFig
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64 Y. Ge, T. Kunz, and L. Lamontits
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66 Y. Ge, T. Kunz, and L. Lamonttha
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68 Y. Ge, T. Kunz, and L. Lamontwhi
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70 Y. Ge, T. Kunz, and L. Lamontver
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Delivering Messagesin Disconnected
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74 R. Shah and N.C. Hutchinson3.1 T
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76 R. Shah and N.C. Hutchinsonset c
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78 R. Shah and N.C. HutchinsonTable
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80 R. Shah and N.C. HutchinsonOracl
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82 R. Shah and N.C. Hutchinsonthe r
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Extending Seamless IP Multicast Edg
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86 P.M. Ruiz et al.Section 4 presen
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88 P.M. Ruiz et al.Access NetworkCo
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90 P.M. Ruiz et al.Access NetworkR
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92 P.M. Ruiz et al.MIGAccess Networ
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94 P.M. Ruiz et al.10.90.81-hop-750
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A Uniform Continuum Model for Scali
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98 E.W. Grundke and A.N. Zincir-Hey
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100 E.W. Grundke and A.N. Zincir-He
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102 E.W. Grundke and A.N. Zincir-He
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Probabilistic Protocols for Node Di
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106 G. Alonso et al.A node discover
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108 G. Alonso et al.frequency alloc
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110 G. Alonso et al.- D is a diagon
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112 G. Alonso et al.and therefore,
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114 G. Alonso et al.complicated. Fo
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Towards Adaptive WLAN Frequency Man
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118 F. Gamba, J.-F. Wagen, and D. R
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Analyzing Split Channel Medium Acce
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130 J. Deng, Y.S. Han, and Z.J. Haa
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Page 187 and 188: 176 G. Calinescuof the UDG 2-hops a
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234 F.J. Molina, J. Barbancho, and
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236 G. Calinescu and P.-J. Wan3.5 4
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238 G. Calinescu and P.-J. Wanmum s
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240 G. Calinescu and P.-J. WanFrom
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242 G. Calinescu and P.-J. Wan5 Alg
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244 G. Calinescu and P.-J. WanThe n
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246 G. Calinescu and P.-J. Wan9. A.
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248 C.J. Colbourn, V.R. Syrotiuk, a
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260 S. Bhadra and A. Ferreirathe mo
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262 S. Bhadra and A. FerreiraIn thi
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264 S. Bhadra and A. FerreiraDefini
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266 S. Bhadra and A. FerreiraThis s
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268 S. Bhadra and A. FerreiraTheore
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270 S. Bhadra and A. Ferreira4. T.
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272 M.K. Denko and Q.H. MahmoudAn i
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274 M.K. Denko and Q.H. Mahmoud3.1
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276 M.K. Denko and Q.H. Mahmoud5. D
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278 B. Macabéo, S. Pierre, and A.
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280 B. Macabéo, S. Pierre, and A.
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282 A. Benslimane and A. BachirIn [
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284 A. Benslimane and A. BachirFig.
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286 A. Benslimane and A. Bachir5 Co
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288 L. Hughes, K. Shumon, and Y. Zh
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3BerlinHeidelbergNew YorkHong KongL
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Series EditorsGerhard Goos, Karlsru
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Organizing CommitteeConference Co-c
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Table of ContentsSpace-Time Routing
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Author IndexAlonso, G. 104Bachir, A
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