Advertisement

Theoretical Aspects of Graph Models for MANETs

  • Josep Díaz
  • Dieter Mitsche
  • Paolo Santi
Chapter
Part of the Monographs in Theoretical Computer Science. An EATCS Series book series (EATCS)

Abstract

We survey the main theoretical aspects of models for mobile ad hoc networks (MANETs). We present theoretical characterizations of mobile network structural properties, different dynamic graph models of MANETs, and finally we give detailed summaries of a few selected articles. In particular, we focus on articles dealing with connectivity of mobile networks and on articles which show that mobility can be used to propagate information between nodes of the network while at the same time maintaining small transmission distances and thus saving energy.

Keywords

Mobility Model Border Effect Pause Time Giant Component Unit Disk Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgement

This research was partially supported by the FP7-ICT-21527 project of the EC, FRONTS. The authors are grateful to the Centre de Recerca Matemàtica, Universitat Autònoma de Barcelona for hospitality and support.

References

  1. 1.
    V. Anand A. Bharathidasas. Sensor Networks: An Overview. Technical Report, Department of Computer Science, University of California at Davis, 2002.Google Scholar
  2. 2.
    C. Avin and G. Ercal. On the cover time and mixing time of random geometric graphs. Theoretical Computer Science, 380(1-2):2–22, 2007.MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    P. K. Agarwal, L. J. Guibas, H. Edelsbrunner, J. Erickson, M. Isard, S. Har-Peled, J. Hershberger, C. Jensen, L. Kavraki, P. Koehl, M. Lin, D. Manocha, D. Metaxas, B. Mirtich, D. Mount, S. Muthukrishnan, D. Pai, E. Sacks, J. Snoeyink, S. Suri, and O. Wolefson. Algorithmic issues in modeling motion. ACM Computing Surveys, 34(4):550–572, 2002.CrossRefGoogle Scholar
  4. 4.
    I. F. Akyildiz, W. Su, Y. Sankarasubramaniam, and E. Cayirci. Wireless sensor networks: a survey. Computer Networks, 38:393–422, 2002.CrossRefGoogle Scholar
  5. 5.
    A. Boukerche and L. Bononi. Simulation and modeling of wireless, mobile, and ad hoc networks. In S. Basagni, M. Conti, S. Giordano, and I. Stojmenović, editors, Mobile Ad Hoc Networking,  chapter 14, pages 373–409. IEEE Press, New York, NY, 2004.Google Scholar
  6. 6.
    C. Bettstetter. Mobility modeling in wireless networks: categorization, smooth movement, and border effects. Mobile Computing and Communications Review, 5(3):55–66, 2001.CrossRefGoogle Scholar
  7. 7.
    C. Bettstetter. Smooth is better than sharp: a random mobility model for simulation of wireless networks. In Proceedings of the 4th ACM International Workshop on Modeling, Analysis and Simulation of Wireless and Mobile Systems, pages 19–27, ACM, New York, 2001.Google Scholar
  8. 8.
    H. Breu and D. G. Kirkpatrick. Unit graph recognition is NP-hard. Computational Geometry, 9:3–24, 1998.MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    C. Bettstetter, G. Resta, and P. Santi. The node distribution of the random waypoint mobility model for wireless ad hoc networks. IEEE Transactions on Mobile Computing, 2(3):257–269, 2003.CrossRefGoogle Scholar
  10. 10.
    T. Camp, J. Boleng, and V. Davies. A survey of mobility models for ad hoc network research. Wireless Communications and Mobile Computing, 2(5):483–502, 2002.CrossRefGoogle Scholar
  11. 11.
    Y. A. Chau and Y.-H. Chen. Analytical link lifetime of a manet based on the three-dimensional brownian mobility model. In Proceedings of the International Symposium on intelligent Signal Processing and Communication Systems, (ISPACS), pages 428–431, IEEE Computer Society, Los Alamitos, CA, 2007.Google Scholar
  12. 12.
    B. N. Clark, C. J. Colbourn, and D. S. Johnson. Unit disk graphs. Discrete Mathematics, 86:165–177, 1990.MATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    A. E. F. Clementi, F. Pasquale, and R. Silvestri. Manets: High mobility can make up for low transmission power. In S. Albers, A. Marchetti-Spaccamela, Y. Matias, S. E. Nikoletseas, and W. Thomas, editors, Proceedings of 36th International Collogquium on Automata, Languages and Programming, pages 387–398, 2009.Google Scholar
  14. 14.
    C. de Morais Cordero and D. P. Agrawal. Ad Hoc and Sensor Networks. World Scientific, New Jersey, 2006.Google Scholar
  15. 15.
    J. Díaz, D. Mitsche, and X. Pérez. Connectivity for dynamic random geometric graphs. IEEE Transactions on Mobile Computing, 8:821–835, 2009.CrossRefGoogle Scholar
  16. 16.
    J. Díaz, D. Mitsche, and X. Pérez. On the probability of existence of mid-size components in random geometric graphs. Advances of Applied Probability, 41:1–14, 2009.CrossRefGoogle Scholar
  17. 17.
    J. Díaz, J. Petit, and M. J. Serna. A random graph model for optical networks of sensors. IEEE Transactions on Mobile Computing, 2:143–154, 2003.CrossRefGoogle Scholar
  18. 18.
    J. Díaz, X. Pérez, M. J. Serna, and N. Wormald. On the walkers problem. SIAM Journal of Discrete Mathematics, 22:747–775, 2008.MATHCrossRefGoogle Scholar
  19. 19.
    S. Dolev, E. Schiller, and J. L. Welch. Random walk for self-stabilizing group communication in ad hoc networks. IEEE Trans. Mobile Computing, 5(7):893–905, 2006.CrossRefGoogle Scholar
  20. 20.
    L. J. Guibas, J. Hershberger, S. Suri, and L. Zhang. Kinetic connectivity for unit disks. Discrete & Computational Geometry, 25:591–610, 2001.MATHMathSciNetGoogle Scholar
  21. 21.
    E. N. Gilbert. Random plane networks. Journal of the Society for Industrial and Applied Mathematics, 9:533–543, 1961.MATHCrossRefGoogle Scholar
  22. 22.
    P. Gupta and P. R. Kumar. Critical power for asymptotic connectivity in wireless networks. In W. McEneaney, G. G. Yin, and Q. Zhang, editors, Stochastic Analysis, Control, Optimization and Applications: A Volume in Honor of W.H. Fleming, pages 547–566. Birkhäuser, 1998.Google Scholar
  23. 23.
    P. Gupta and P. R. Kumar. The capacity of wireless networks. IEEE Transactions on Information Theory, 46:388–404, 2000.MATHCrossRefMathSciNetGoogle Scholar
  24. 24.
    M. C. Golumbic. Algorithmic Graph Theory and Perfect Graphs. Academic Press, New York, NY, 1980.MATHGoogle Scholar
  25. 25.
    A. Goel, S. Rai, and B. Krishnamachari. Sharp thresholds for monotone properties in random geometric graphs. Annals of Applied Probability, 15:364–370, 2005.MathSciNetGoogle Scholar
  26. 26.
    G. Grimmett and D. Stirzaker. Probability and Random Processes. Oxford University Press, 2001.Google Scholar
  27. 27.
    M. Grossglauser and D. N. C. Tse. Mobility increases the capacity of ad hoc wireless networks. IEEE/ACM Transactions on Networking, 10(4):477–486, 2002.CrossRefGoogle Scholar
  28. 28.
    R. A. Guerin. Channel occupancy time distribution in a cellular radio system. IEEE Transactions on Vehicular Technology, 36(3):89–99, 1987.CrossRefGoogle Scholar
  29. 29.
    S. Guo and O. W. W. Yang. Energy-aware multicasting in wireless ad hoc networks: A survey and discussion. Computer Communications, 30:2129–2148, 2007.CrossRefGoogle Scholar
  30. 30.
    P. G. Hall. Introduction to the Theory of Coverage Processes. Wiley, New York, NY, 1988.MATHGoogle Scholar
  31. 31.
    R. Hekmat. Ad-hoc Networks: Fundamental Properties and Network Topologies. Springer, Heidelberg, 2006.Google Scholar
  32. 32.
    X. Hong, M. Gerla, G. Pei, and C.-C. Chiang. A group mobility model for ad hoc wireless networks. In Proceedings of the 2nd ACM international workshop on Modeling, Analysis and Simulation of Wireless and Mobile Systems (MSWiM), pages 53–60, ACM, New York, NY, 1999.Google Scholar
  33. 33.
    E. Hyytiä, P. Lassila, and J. Virtamo. Spatial node distribution of the random waypoint mobility model with applications. IEEE Transactions on Mobile Computing, 5(6):680–694, 2006.CrossRefGoogle Scholar
  34. 34.
    M. Hollick, I. Martinovic, T. Krop, and I. Rimac. A survey on dependable routing in sensor networks, ad hoc networks, and cellular networks. In EUROMICRO Conference, pages 495–502, Los Alamitos, CA, 2004. IEEE Computer Society.Google Scholar
  35. 35.
    Z. J. Haas and M. R. Pearlman. The performance of query control schemes for the zone routing protocol. IEEE/ACM Transactions on Networking, 9(4):427–438, 2001.CrossRefGoogle Scholar
  36. 36.
    A. P. Jardosh, E. M. Belding-Royer, K. C. Almeroth, and S. Suri. Real-world environment models for mobile network evaluation. IEEE Journal on Selected Areas in Communications, 23(3):622–632, 2005.CrossRefGoogle Scholar
  37. 37.
    D. B. Johnson and D. A. Maltz. Dynamic source routing in ad hoc wireless networks. In Mobile Computing, pages 153–181. Kluwer Academic Publishers, 1996.Google Scholar
  38. 38.
    P. Jacquet, B. Mans, and G. Rodolakis. Information propagation speed in mobile and delay tolerant networks. In Proceeding of the 29th Annual Joint Conference of the IEEE Computer and Communications Societies (INFOCOM), Los Alamitos, CA, 2009. IEEE Computer Society.Google Scholar
  39. 39.
    L. M. Kirousis, E. Kranakis, D. Krizanc, and A. Pelc. Power consumption in packet radio networks. Theoretical Computer Science, 243(1-2):289–305, 2000.MATHCrossRefMathSciNetGoogle Scholar
  40. 40.
    S. Kumar, T.-H. Lai, and J. Balogh. On k-coverage in a mostly sleeping sensor network. Wireless Networks, 14:277–294, 2008.CrossRefGoogle Scholar
  41. 41.
    W. Kieß and M. Mauve. A survey on real-world implementations of mobile ad-hoc networks. Ad Hoc Networks, 5:324–339, 2007.CrossRefGoogle Scholar
  42. 42.
    X.-Y. Li. Topology control in wireless ad hoc networks. In S. Basagni, M. Conti, S. Giordano, and I. Stojmenović, editors, Mobile Ad Hoc Networking,  chapter 6, pages 175–204. IEEE Press, New York, NY, 2004.Google Scholar
  43. 43.
    J.-Y. LeBoudec and M. Vojnović. The random trip model: Stability, stationary regime, and perfect simulation. IEEE/ACM Transactions on Networking, 14:1153–1166, 2006.CrossRefGoogle Scholar
  44. 44.
    S. Meguerdichian, F. Koushanfar, M. Potkonjak, and M. B. Srivastava. Coverage problems in wireless ad-hoc sensor networks. In Proceeding of the 19th Annual Joint Conference of the IEEE Computer and Communications Societies (INFOCOM), pages 1380–1387, 2001.Google Scholar
  45. 45.
    M. D. Penrose. The longest edge of the random minimal spanning tree. The Annals of Applied Probability, 7:340–361, 1997.MATHCrossRefMathSciNetGoogle Scholar
  46. 46.
    M. D. Penrose. On the k-connectivity for a geometric random graph. Random Structures & Algorithms, 15(2):145–164, 1999.MATHCrossRefMathSciNetGoogle Scholar
  47. 47.
    M. D. Penrose. Random Geometric Graphs. Oxford University Press, Oxford, 2003.MATHCrossRefGoogle Scholar
  48. 48.
    J. Pitman. Probability. Springer, New York, NY, 1999.Google Scholar
  49. 49.
    R. Rajaraman. Topology control and routing in ad hoc networks: A survey. SIGACT News, 33:60–73, 2002.CrossRefGoogle Scholar
  50. 50.
    E. M. Royer and C-K. Toh. A review of current routing protocols for ad-hoc mobile wireless networks. IEEE Personal Communications, 7:46–55, 1999.CrossRefGoogle Scholar
  51. 51.
    P. Santi. The critical transmitting range for connectivity in mobile ad hoc networks. IEEE Transactions Mobile Computing, 4(3):310–317, 2005.CrossRefGoogle Scholar
  52. 52.
    P. Santi. Topology control in wireless ad hoc and sensor networks. ACM Computing Surveys, 37:164–194, 2005.CrossRefGoogle Scholar
  53. 53.
    P. Santi and D. M. Blough. The critical transmitting range for connectivity in sparse wireless ad hoc networks. IEEE Transactions on Mobile Computing, 2(1):25–39, 2003.CrossRefGoogle Scholar
  54. 54.
    P. Santi, D. M. Blough, and F. S. Vainstein. A probabilistic analysis for the range assignment problem in ad hoc networks. In Proceedings of the 2nd ACM International Symposium on Mobile Ad Hoc Networking and Computing, (MobiHoc), pages 212–220, 2001.Google Scholar
  55. 55.
    A. Sen and M. L. Huson. A new model for scheduling packet radio networks. In Proceedings of the 15th Annual Joint Conference of the IEEE Computer and Communications Societies (INFOCOM), IEEE Computer Society, Los Alamitos, CA, 1997.Google Scholar
  56. 56.
    S. Schmid and R. Wattenhofer. Algorithmic models for sensor networks. In Proceedings of the 20th International Parallel and Distributed Processing Symposium (IPDPS), IEEE Computer Society, Los Alamitos, CA, 2006.Google Scholar
  57. 57.
    S. Tilak, N. B. Abu-Ghazaleh, and W. Heinzelman. A taxonomy of sensor network communication models. Mobile Computing and Communication Review, 6:28–36, 2002.CrossRefGoogle Scholar
  58. 58.
    J. Tian, J. Hahner, C. Becker, I. Stepanov, and K. Rothermel. Graph-based mobility model for mobile ad hoc network simulation. In Proceedings. 35th Annual Simulation Symposium, IEEE Computer Society, Los Alamitos, CA, 2002.Google Scholar
  59. 59.
    E. J. van Leeuwen. Optimization and Approximation on Systems of Geometric Objects. PhD thesis, Universiteit van Amsterdam, 2009.Google Scholar
  60. 60.
    W. Wang, V. Srinivasan, and K.-C. Chua. Trade-offs between mobility and density for coverage in wireless sensor networks. In Proceedings of the 13th annual ACM international conference on Mobile computing and networking (MobiCom), pages 39–50, ACM, New York, 2007.Google Scholar
  61. 61.
    P.-J. Wan and C.-W. Yi. Asymptotic critical transmission radius and critical neighbor number for -connectivity in wireless ad hoc networks. In J. Murai, C. E. Perkins, and L. Tassiulas, editors, Proceedings of the 5th ACM Interational Symposium on Mobile Ad Hoc Networking and Computing, pages 1–8. ACM, New York, NY, 2004.CrossRefGoogle Scholar
  62. 62.
    P.-J. Wan and C.-W. Yi. Coverage by randomly deployed wireless sensor networks. IEEE Transaction on Information Theory, 52(6):2658–2669, 2006.CrossRefMathSciNetGoogle Scholar
  63. 63.
    X.Wang, G. Xing, Y. Zhang, C. Lu, R. Pless, and C. Gill. Integrated coverage and connectivity configuration in wireless sensor networks. In Proceedings of ACM SenSys, pages 28–39, 2003.Google Scholar
  64. 64.
    J. Yoon, M. Liu, and B. Noble. Random waypoint considered harmful. In Proceeding of he 21st Annual Joint Conference of the IEEE Computer and Communications Societies (INFOCOM), IEEE Computer Society, Los Alamitos, CA, 2003.Google Scholar
  65. 65.
    J. Yoon, M. Liu, and B. Noble. Sound mobility models. In D. B. Johnson, A. D. Joseph, and N. H. Vaidya, editors, Proceedings of the Ninth Annual International Conference on Mobile Computing and Networking (MOBICOM), pages 205–216. ACM, New York, NY, 2003.Google Scholar
  66. 66.
    J. Yick, B. Mukherjee, and D. Ghosal. Wireless sensor network survey. Computer Networks, 52:2292–2330, 2008.CrossRefGoogle Scholar
  67. 67.
    F. Zhao and L. Guibas, editors. Distributed Environmental Monitoring Using Random Sensor Networks, vol. 2634, Lecture Notes in Computer Science. Springer, 2003.Google Scholar
  68. 68.
    H. Zang and J. Hou. On deriving the upper bound of alpha-lifetime for large sensor networks. In J. Murai, C. E. Perkins, and L. Tassiulas, editors, Proceedings of the 5th ACM Interational Symposium on Mobile Ad Hoc Networking and Computing, pages 16–24. ACM, New York, NY, 2004.Google Scholar
  69. 69.
    Z. Zhang. Routing in intermittently connected mobile ad hoc networks and delay tolerant networks: Overview and challenges. IEEE Communications Surveys and Tutorials, 8(1-4):24–37, 2006.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.Departament de Llenguatges, Sistemes i InformàticsUniversitat Politècnica de Catalunya Grup de Recerca ALBCOMBarcelonaSpain
  2. 2.Universitat Politecnica de Catalunya Grup de Recerca ALBCOMBarcelonaSpain
  3. 3.Istituto di Informatica e Telematica del CNRPisaItaly

Personalised recommendations