Skip to main content
SpringerLink
Log in

Ad hoc networks beyond unit disk graphs

  • Published:
Wireless Networks Aims and scope Submit manuscript

Abstract

In this paper, we study an algorithmic model for wireless ad hoc and sensor networks that aims to be sufficiently close to reality as to represent practical realworld networks while at the same time being concise enough to promote strong theoretical results. The quasi unit disk graph model contains all edges shorter than a parameter d between 0 and 1 and no edges longer than 1. We show that—in comparison to the cost known for unit disk graphs—the complexity results of geographic routing in this model contain the additional factor 1/d 2. We prove that in quasi unit disk graphs flooding is an asymptotically message-optimal routing technique, we provide a geographic routing algorithm being most efficient in dense networks, and we show that classic geographic routing is possible with the same asymptotic performance guarantees as for unit disk graphs if \(d\ge 1/\sqrt{2}\).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Abraham, I., Dolev, D., & Malkhi D. (2004). LLS: A locality aware location service for mobile ad hoc networks. In DIALM-POMC ’04: Proceedings of the 2004 Joint workshop on Foundations of Mobile Computing, pp. 75–84.

  2. Alzoubi, K., Wan, P. -J., & Frieder, O. (2002). Message-optimal connected dominating sets in mobile ad hoc networks. In Proceedings of the 3rd ACM International Symposium on Mobile ad hoc networking & computing (MOBIHOC).

  3. Awerbuch, B. (1985). Complexity of Network Synchronization. Journal of the ACM (JACM), 32(4), 804–823.

    Article  MATH  MathSciNet  Google Scholar 

  4. Awerbuch, B., & Peleg, D. (1990). Network synchronization with polylogarithmic overhead. In Proceedings of the 31st IEEE Symposium on Foundations of Computer Science (FOCS), pp. 514–522.

  5. Barrière, L., Fraigniaud, P., & Narayanan, L. (2001). Robust position-based routing in wireless ad hoc networks with unstable transmission ranges. In Proceedings of the 5th International Workshop on Discrete Algorithms and Methods for Mobile Computing and Communications (DIAL-M) (pp. 19–27). ACM Press.

  6. Basagni, S., Chlamtac, I., Syrotiuk, V., & Woodward, B. (1998). A distance routing effect algorithm for mobility (DREAM). In Proceedings of the 4th Annual International Conference on Mobile Computing and Networking (MOBICOM) (pp. 76–84). Dallas, TX, USA: ACM Press.

  7. Boone, P., Chavez, E., Gleitzky, L., Kranakis, E., Opatrny, J., Salazar, G., & Urrutia, J. (2004). Morelia test: Improving the efficiency of the gabriel test and face routing in ad-hoc networks. In Proceedings of the 11th Colloquium on Structural Information and Communication Complexity (SIROCCO), Smolenice Castle, Slovakia.

  8. Bose, P., Brodnik, A., Carlsson, S., Demaine, E., Fleischer, R., López-Ortiz, A., Morin, P., & Munro, J. (2000). Online routing in convex subdivisions. In International Symposium on Algorithms and Computation (ISAAC), vol. 1969 of Lecture Notes in Computer Science (pp. 47–59). Springer.

  9. Bose, P., & Morin, P. (1999). Online routing in triangulations. In Proceedings of 10th International Symposium on Algorithms and Computation (ISAAC), Vol. 1741 of Springer LNCS, pp. 113–122.

  10. Bose, P., Morin, P., Stojmenovic, I., & Urrutia, J. (1999). Routing with guaranteed delivery in ad hoc wireless networks. In Proceedings of the 3rd International Workshop on Discrete Algorithms and Methods for Mobile Computing and communications (DIAL-M), pp. 48–55.

  11. Burkhart, M., von Rickenbach, P., Wattenhofer, R., & Zollinger, A. (2004). Does topology control reduce interference? In Proceedings of the 5th ACM International Symposium on Mobile Ad-Hoc Networking and Computing (MobiHoc), pp. 9–19.

  12. Chang, E. (1982). Echo algorithms: Depth parallel operations on general graphs. IEEE Transactions on Software Engineering, 8, 391–401

    Google Scholar 

  13. Cruz, R., & Santhanam, A. (2003). Optimal routing, link scheduling, and power control in multi-hop wireless networks. In Proceedings of the 22nd Annual Joint Conference of the IEEE Computer and Communications Societies INFOCOM).

  14. Datta, S., Stojmenovic, I., & Wu, J. (2002). Internal node and shortcut based routing with guaranteed delivery in wireless networks. In Cluster computing 5 (pp. 169–178). Kluwer Academic Publishers.

  15. ElBatt, T., & Ephremides, A. (2002). Joint scheduling and power control for wireless ad-hoc networks. In Proceedings of the 21st Annual Joint Conference of the IEEE Computer and Communications Societies (INFOCOM).

  16. Ephremides, A., & Truong, T. (1990). Scheduling broadcasts in multihop radio networks. IEEE Transactions on Communications, 38, 456–460.

    Article  Google Scholar 

  17. Finn, G. (1987). Routing and addressing problems in large metropolitan-scale internetworks. Technical Report ISI/RR-87-180, USC/ISI, March 1987.

  18. Flury, R., & Wattenhofer, R. (2006). MLS: An efficient location service for mobile ad hoc networks. In 7th ACM International Symposium on Mobile Ad Hoc Networking and Computing (MOBIHOC), Florence, Italy, May.

  19. Frey, H. (2005). Geographical cluster based multihop ad hoc network routing with guaranteed delivery. In 2nd IEEE International Conference on Mobile Ad Hoc and Sensor Systems (MASS), Washington, DC, USA, November.

  20. Fussen, M., Wattenhofer, R., & Zollinger, A. (2005). Interference arises at the receiver. In International Conference on Wireless Networks, Communications, and Mobile Computing (WIRELESSCOM), Maui, Hawaii, USA, June.

  21. Gabriel, K., & Sokal, R. (1969). A new statistical approach to geographic variation analysis. Systematic Zoology, 8, 259–278.

    Article  Google Scholar 

  22. Gao, J., Guibas, L., Hershberger, J., Zhang, L., & Zhu, A. (2001). Discrete mobile centers. In Proceedings 17th Annual Symposium on Computational Geometry (SCG) (pp. 188–196). Medford, MA, USA: ACM Press.

  23. Gao, J., Guibas, L., Hershberger, J., Zhang, L., & Zhu, A. (2001). Geometric spanner for routing in mobile networks. In Proceedings of the 2nd ACM International Symposium on Mobile Ad Hoc Networking & Computing (pp 45–55). Long Beach, CA, USA: ACM Press.

  24. Grönkvist, J. (2005). Interference-based scheduling in spatial Reuse TDMA. PhD thesis, Royal Institute of Technology, Stockholm, Sweden.

  25. Hou, T., & Li, V. (1986). Transmission range control in multihop packet radio networks. IEEE Transactions on Communications, 34(1), 38–44.

    Article  Google Scholar 

  26. Huang, H., Richa, A. W., & Segal, M. (2002). Approximation algorithms for the mobile piercing set problem with applications to clustering in ad-hoc networks. In Proceedings of the 6th International Workshop on Discrete Algorithms and Methods for Mobile Computing and Communications (DIAL-M), Atlanta, Georgia, USA, pp. 52–61.

  27. Jain, K., Padhye, J., Padmanabhan, V., & Qiu, L. (2003). Impact of interference on multi-hop wireless network performance. In Proceedings of the 9th Annual International Conference on Mobile Computing and Networking (MOBICOM).

  28. Jia L., Rajaraman R., & Suel R. (2001). An efficient distributed algorithm for constructing small dominating sets. In Proceedings of the 20th ACM Symposium on Principles of Distributed Computing (PODC), 2001, pp 33–42.

  29. Johnson, D. B., & Maltz, D. A. (1996). Dynamic source routing in ad hoc wireless networks. In Imielinski & Korth (Eds.), Mobile computing, Vol. 353. Kluwer Academic Publishers.

  30. Karp, B., & Kung, H. (2000). GPSR: Greedy perimeter stateless routing for wireless networks. In Proceedings of the 6th Annual International Conference on Mobile Computing and Networking (MOBICOM), pp. 243–254.

  31. Kim, Y. -J., Govindan, R., Karp, B., & Shenker, S. (2005). Geographic routing made practical. In Proceedings of the Second USENIX/ACM Symposium on Networked System Design and Implementation (NSDI 2005), Boston, Massachusetts, USA, May.

  32. Kim, Y. -J., Govindan, R., Karp, B., & Shenker, S. (2005). On the pitfalls of geographic face routing. In Proceedings of the ACM Joint Workshop on Foundations of Mobile Computing (DIALM-POMC), Cologne, Germany, September.

  33. Ko, Y. -B., & Vaidya, N. (1998). Location-aided routing (LAR) in mobile a hoc networks. In Proceedings of the 4th Annual International Conference on Mobile Computing and Networking (MOBICOM), pp. 66–75.

  34. Kothapalli, K., Scheideler, C., Onus, M., & Richa, A. (2005). Constant density spanners for wireless ad-hoc networks. In Proceedings of the 17th Annual ACM Symposium on Parallelism in Algorithms and Architectures (SPAA).

  35. Kranakis, E., Singh, H., & Urrutia, J. (1999). Compass routing on geometric networks. In Proceedings 11th Canadian Conference on Computational Geometry, Vancouver, August, pp. 51–54.

  36. Kuhn, F., Moscibroda, T., Nieberg, T., & Wattenhofer, R. (2005). Fast deterministic distributed maximal independent set computation on growth-bounded graphs. In 9th International Symposium on Distributed Computing (DISC), Cracow, Poland, September.

  37. Kuhn, F., Moscibroda, T., Nieberg, T., & Wattenhofer, R. (2005). Local approximation schemes for ad hoc and sensor networks. In Proceedings of the 3rd ACM Joint Workshop on Foundations of Mobile Computing (DIALM-POMC), Cologne, Germany, September.

  38. Kuhn, F., Moscibroda, T., Nieberg, T., & Wattenhofer, R. (2005). Local approximation schemes for ad hoc and sensor networks. In 3rd ACM Joint Workshop on Foundations of Mobile Computing (DIALM-POMC), Cologne, Germany, September.

  39. Kuhn, F., Moscibroda, T., & Wattenhofer, R. (2004). Initializing newly deployed ad hoc and sensor networks. In 10th Annual International Conference on Mobile Computing and Networking (MOBICOM), Philadelphia, Pennsylvania, USA, September.

  40. Kuhn, F., Moscibroda, T., & Wattenhofer, R. (2004). Radio network clustering from scratch. In Proceedings of the 12th Annual European Symposium on Algorithms (ESA), Bergen, Norway, September.

  41. Kuhn, F., Moscibroda, T., & Wattenhofer, R. (2004). Unit disk graph approximation. In 2nd ACM Joint Workshop on Foundations of Mobile Computing (DIALM-POMC), Philadelphia, Pennsylvania, USA, October.

  42. Kuhn, F., Moscibroda, T., & Wattenhofer, R. (2005). On the locality of bounded growth. In 24th ACM Symposium on the Principles of Distributed Computing (PODC), Las Vegas, Nevada, USA, July.

  43. Kuhn, F., & Wattenhofer, R. (2003). Constant-time distributed dominating set approximation. In Proceedings of the 22nd ACM Symposium on the Principles of Distributed Computing (PODC), Boston, Massachusetts, USA.

  44. Kuhn, F., Wattenhofer, R., Zhang, Y., & Zollinger, A. (2003). Geometric routing: Of theory and practice. In Proceedings of the 22nd ACM Symposium on the Principles of Distributed Computing (PODC), Boston, Massachusetts, USA.

  45. Kuhn, F., Wattenhofer, R., & Zollinger, A. (2002). Asymptotically optimal geometric mobile ad-hoc routing. In Proceedings of the 6th International Workshop on Discrete Algorithms and Methods for Mobile Computing and Communications (DIAL-M) (pp 24–33). Atlanta, GA, USA: ACM Press.

  46. Kuhn, F., Wattenhofer, R., & Zollinger, A. (2003). Ad-Hoc networks beyond unit disk graphs. In 1st ACM Joint Workshop on Foundations of Mobile Computing (DIALM-POMC), San Diego, California, USA, September.

  47. Kuhn, F., Wattenhofer, R., & Zollinger, A. (2003). Worst-case optimal and average-case efficient geometric ad-hoc routing. In Proceedings of the 4th ACM Int. Symposium on Mobile Ad-Hoc Networking and Computing (MOBIHOC), Annapolis, Maryland, USA.

  48. Leong, B., Liskov, B., & Morris, R. (2006). Geographic routing without planarization. In 3rd Symposium on Networked Systems Design & Implementation (NSDI), San Jose, California, USA, May.

  49. Leong, B., Mitra, S., & Liskov, B. (2005). Path vector face routing: Geographic routing with local face information. In 13th IEEE International Conference on Network Protocols (ICNP), Boston, Massachusetts, USA, November.

  50. Li, J., Jannotti, J., De Couto, D., Karger, D., & Morris, R. (2000). A scalable location service for geographic ad hoc routing. In Proceedings of the 6th ACM International Conference on Mobile Computing and Networking (MobiCom), pp. 120–130, Aug.

  51. Li X.-Y., Calinescu G., & Wan P.-J. (2002). Distributed construction of planar spanner and routing for ad hoc wireless networks. In Proceedings of the 21st Annual Joint Conference of the IEEE Computer and Communications Societies (INFOCOM), New York, NY, USA.

  52. Li, X. -Y., Song, W. -Z., & Wang, Y. (2004). Localized topology control for heterogenous wireless ad hoc networks. In Proceedings of the 1st IEEE International Conference on Mobile Ad-hoc and Sensor Systems (MASS), Fort Lauderdale, Florida, USA, October.

  53. Moscibroda, T., Oswald, Y. A., & Wattenhofer, R. (2007). How optimal are wireless scheduling protocols? In Proceedings of the 26th Annual Joint Conference of the IEEE Computer and Communications Societies (INFOCOM), Anchorage, Alaska, USA, May.

  54. Moscibroda T., von Rickenbach P., & Wattenhofer R. (2006). Analyzing the energy-latency trade-off during the deployment of sensor networks. In Proceedings of the 25th Annual Joint Conference of the IEEE Computer and Communications Societies (INFOCOM), Barcelona, Spain, April.

  55. Moscibroda, T., & Wattenhofer, R. (2005). Coloring unstructured radio networks. In Proceedings of the 17th ACM Symposium on Parallelism in Algorithms and Architectures (SPAA), Las Vegas, Nevada, USA, July.

  56. Moscibroda, T., & Wattenhofer, R. (2005). Maximal independent sets in radio networks. In Proceedings of the 24th ACM Symposium on the Principles of Distributed Computing (PODC), Las Vegas, Nevada, USA, July.

  57. Moscibroda, T., & Wattenhofer, R. (2005). Minimizing interference in ad hoc and sensor networks. In Proceedings of the International Workshop on Discrete Algorithms and Methods for Mobile Computing and Communications (DIALM), pp. 24–33.

  58. Moscibroda, T., & Wattenhofer, R. (2006). The complexity of connectivity in wireless networks. In Proceedings of the 25th Annual Joint Conference of the IEEE Computer and Communications Societies (INFOCOM), Barcelona, Spain, April.

  59. Moscibroda, T., Wattenhofer, R., & Zollinger A. (2006). Topology control meets SINR: The scheduling complexity of arbitrary topologies. In 7th ACM International Symposium on Mobile Ad Hoc Networking and Computing (MOBIHOC), Florence, Italy, May.

  60. O’Dell, R., & Wattenhofer, R. (2005). Theoretical aspects of connectivity-based multi-hop positioning. Theoretical Computer Science, 344(1), 47–68, November.

    Article  MATH  MathSciNet  Google Scholar 

  61. Peleg, D. (2000). Distributed computing, a locality-sensitive approach. Philadelphia, PA, USA: Society for Industrial and Applied Mathematics.

  62. Peleg, D., & Schäffer, A. A. (1989). Graph spanners. Journal of Graph Theory, 13(1), 99–116.

    Article  MATH  MathSciNet  Google Scholar 

  63. Perkins, C., & Royer, E. (1999). Ad-hoc on-demand distance vector routing. In Proceedings of the 2nd IEEE Workshop on Mobile Computing Systems and Applications, pp. 90–100.

  64. Rajaraman, R. (2002). Topology control and routing in ad hoc networks: A survey. SIGACT News 33:60–73, June

    Article  Google Scholar 

  65. Santi, P. (2005). Topology control in wireless ad hoc and sensor networks. ACM Computing Surveys (CSUR), 37(2), 164–194, June.

    Article  Google Scholar 

  66. Schmid, S., & Wattenhofer, R. (2006). Algorithmic models for sensor networks. In Proceedings of the 14th International Workshop on Parallel and Distributed Real-Time Systems (WPDRTS), Island of Rhodes, Greece, April.

  67. Takagi, H., & Kleinrock, L. (1984). Optimal transmission ranges for randomly distributed packet radio terminals. IEEE Transactions on Communications, 32(3), 246–257.

    Article  Google Scholar 

  68. Toussaint, G. (1980). The relative neighborhood graph of a finite planar set. Pattern Recognition, 12(4), 261–268.

    Article  MATH  MathSciNet  Google Scholar 

  69. Urrutia, J. (2005). Routing with guaranteed delivery in geometric and wireless networks. In: Stojmenovic, I. (Ed.), Handbook of Wireless Networks and Mobile Computing, chapter 18 (pp. 393–406). John Wiley & Sons.

  70. von Rickenbach, P., Schmid, S., Wattenhofer, R., & Zollinger, A. (2005). A robust interference model for wireless ad-hoc networks. In Proceedings of the 5th International Workshop on Algorithms for Wireless, Mobile, Ad Hoc and Sensor Networks (WMAN), Denver, Colorado, USA, April.

  71. Wang, Y., & Li, X. -Y. (2002). Geometric spanners for wireless ad hoc networks. In Proceedings of the 22nd International Conference on Distributed Computing Systems (ICDCS).

  72. Wang, Y., & Li, X. -Y. (2003). Localized construction of bounded degree planar spanner. In Proceedings of the 1st DIALM-POMC Joint Workshop on Foundations of Mobile Computing, San Diego, California, USA.

  73. Wattenhofer, R., Li, L., Bahl, P., & Wang, Y.-M. (2001). Distributed topology control for power efficient operation in multihop wireless ad hoc networks. In Proceedings of the 20th Annual Joint Conference of the IEEE Computer and Communications Societies (INFOCOM), pp. 1388–1397

  74. Zollinger, A. (2005). Networking unleashed: Geographic routing and topology control in ad hoc and sensor networks. PhD thesis, ETH Zurich, Switzerland, Diss. ETH 16025.

Download references

Author information

Authors and Affiliations

  1. Microsoft Research, Mountain View, CA, 94043, USA

    Fabian Kuhn

  2. ETH Zurich, 8092, Zurich, Switzerland

    Roger Wattenhofer

  3. Department of Electrical Engineering and Computer Science, University of California, 513 Soda Hall #1776, Berkeley, CA, 94720-1776, USA

    Aaron Zollinger

Authors
  1. Fabian Kuhn
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Roger Wattenhofer
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Aaron Zollinger
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Aaron Zollinger.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kuhn, F., Wattenhofer, R. & Zollinger, A. Ad hoc networks beyond unit disk graphs. Wireless Netw 14, 715–729 (2008). https://doi.org/10.1007/s11276-007-0045-6

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11276-007-0045-6

Keywords

Search

Navigation