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Computing 2-Hop Neighborhoods in Ad Hoc Wireless Networks 185unit-disk graph. We need at least the distance in between any pair of adjacentnodes. Same arguments using rigid pieces apply when a node is able to computethe angle in between the segments to adjacent nodes. However, without any geographicalknowledge we do not know whether it is possible to compute 2-hopneighborhoods with O(n) messages each having O(log n) bits. This observationraises the interesting question whether there are any (meaningful) problemswhich have higher communication complexity on unit-disk graphs than on embedded(nodes aware of their geographical position) unit-disk graphs. Note thatit is NP-Hard to recognize unit-disk graphs [7].However, it follows from standard algebraic geometry results (page 542 of[17] or improved bounds in [4]) that the number of labeled unit-disk graphs of nnodes is between 2 c1n log n and 2 c2n log n , for constants c 1 and c 2 and therefore aprotocol with a total O(n log n) bits communication complexity is possible. AnO(n log n) bits communication complexity would follow from a solution to anopen problem in algebraic geometry [5]. It is worth mentioning that algebraicgeometry solutions seem to have huge running time and space complexity.Our model does not account for messages lost because of interference. Itwould be desirable to design synchronous distributed algorithms with low messagecomplexity and low time complexity in a model where messages are losteither due to signal interference or due to node overloading.AcknowledgmentsThe author thanks Peng-Jun Wan and Xiang-Yang Li, who inspired this paper bypresenting their results. The author thanks Sougata Basu, Adrian Dumitrescu,and Peter Sanders for insight in the issue of extending the results to case whengeographical knowledge is not available.References1. Khaled M. Alzoubi, “Distributed Algorithms for Connected Dominating Set inWireless Ad Hoc Networks”, Illinois Institute of Technology, 2002.2. Khaled M. Alzoubi, Peng-Jun Wan and Ophir Frieder, “Message-Optimal ConnectedDominating Sets in Mobile Ad Hoc Networks”, in ACM MOBIHOC ’02.3. L. Bao and J. J. Garcia-Luna-Aceves, “Channel Access Scheduling in Ad HocNetworks with Unidirectional Links”, 5th International Workshop on Discrete Algorithmsand Methods for Mobility, 2001, Pages 9–18.4. S. Basu “Different bounds on the different Betti numbers of semi-algebraic sets”,to appear in Discrete and Computational Geometry. Available athttp://www.math.gatech.edu/˜saugata/.5. S. Basu, R. Pollack, and M. F. Roy, Algorithms in Real Algebraic Geometry,Springer-Verlag, 2003.6. V. Bharghavan and B. Das, “Routing in Ad Hoc Networks Using Minimum ConnectedDominating Sets”, International Conference on Communications’97, Montreal,Canada. June 1997.
186 G. Calinescu7. Heinz Breu and David G. Kirkpatrick. “Unit disk graph recognition is NP-hard”,Computational Geometry. Theory and Applications, 9:3–24, 1998.8. T. Calamoneri and R. Petreschi, “L(2,1)-Labeling of Planar Graphs”, 5th InternationalWorkshop on Discrete Algorithms and Methods for Mobility, 2001, Pages28–33.9. G. Calinescu, I. Mandoiu, P.-J. Wan, and A. Zelikovsky, “Selecting ForwardingNeighbors in Wireless Ad Hoc Networks”, 5th International Workshop on DiscreteAlgorithms and Methods for Mobility, 2001, Pages 34–43.10. I. Chlamtac and S. Pinter, “Distributed Nodes Organization Algorithm for ChannelAccess in a Multihop Dynamic Radio Network”, IEEE Trans. on Computers,36(6):728–737, 1987.11. B. N. Clark, C. J. Colbourn, and D. S. Johnson, “Unit Disk Graphs”, DiscreteMathematics, 86:165–177, 1990.12. J. R. Griggs and R. K. Yeh, “Labeling Graphs with a Condition at Distance 2”,SIAM J. Disc. Math, 5:586–595, 1992.13. J. Hightower and G Borriello, “Location Systems for Ubiquitous Computing”,IEEE Computer, vol. 34(8), 2001, pp 57–66.14. P. Jacquet, A. Laouiti, P. Minet, and L. Viennot, “Performance analysis of OLSRmultipoint relay flooding in two ad hoc wireless network models”, in RSRCP,Special issue on Mobility and Internet, 2001.15. K. Krizman, T. Bieda, and T. Rappaport, “Wireless position location: fundamentals,implementation strategies, and source of error”, Veh. Tech. Conf, 1997, 919–923.16. M. V. Marathe, H. Breu, H. B. Hunt III, S. S. Ravi and D. J. Rosenkrantz, ”SimpleHeuristics for Unit Disk Graphs”, Networks, Vol. 25, 1995, pp. 59–68.17. B. Mishra, “Computational Real Algebraic Geometry” in Handbook of Discreteand Computational Geometry, J. E. Goodman and J. O’Rourke (editors), CRCPress, 1997.18. A. Nasipuri and K. Lim “A Directionality based Location Discovery Scheme forWireless Sensor Networks”, WSNA 2002.19. S. Ramanathan and M. Steenstrup, “A survey of routing techniques for mobilecommunication networks”, ACM/Baltzer Mobile Networks and Applications, 89–104, 1996.20. I Stojmenovic and X. Lin, “Loop-free hybrid single-path/flooding routing algorithmswith guaranteed delivery for wireless networks”, IEEE Transactions onParallel and Distributed Systems, 12:1023–1032, 2001.21. Peng-Jun Wan, Khaled M. Alzoubi, and Ophir Frieder “Distributed Constructionof Connected Dominating Set in Wireless Ad Hoc Networks”, in IEEE INFOCOM2002.22. Yu Wang and Xiang-Yang Li, “Geometric Spanners for Wireless Ad Hoc Networks”,in ICDCS 2002.23. W. Whiteley “Rigidity and Scene Analysis”, Handbook of Discrete and ComputationalGeometry, 893–916, ed. J. E. Goodman and J. O’Rourke, CRC Press, 1997.24. J. Wu and H.L. Li, “On calculating connected dominating set for efficient routingin ad hoc wireless networks”, Proceedings of the 3rd ACM international workshopon Discrete algorithms and methods for mobile computing and communications,1999, Pages 7–14.
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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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18 J. Doshi and P. Kilambibandwidth
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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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Extending Seamless IP Multicast Edg
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88 P.M. Ruiz et al.Access NetworkCo
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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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132 J. Deng, Y.S. Han, and Z.J. Haa
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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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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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