Skip to main content
SpringerLink
Log in

Approximation and Heuristic Algorithms for Computing Backbones in Asymmetric Ad-hoc Networks

  • Published:
Theory of Computing Systems Aims and scope Submit manuscript

Abstract

We consider the problem of dominating set-based virtual backbone used for routing in asymmetric wireless ad-hoc networks. These networks have non-uniform transmission ranges and are modeled using directed disk graphs. The corresponding graph theoretic problem seeks a strongly connected dominating-absorbent set of minimum cardinality in a digraph. A subset of nodes in a digraph is a strongly connected dominating-absorbent set if the subgraph induced by these nodes is strongly connected and each node in the graph is either in the set or has both an in-neighbor and an out-neighbor in it. Due to the dynamic nature of ad-hoc networks, distributed algorithms for this problem are of practical significance. Hence, we seek algorithms that do not require centralized computation and yet yield good approximation factors and/or behave well in practice. We present a first distributed approximation algorithm for this problem. The algorithm achieves a constant approximation ratio if the ratio of the maximum transmission range over the minimum transmission range in the network is bounded and takes O(Diam) rounds, where Diam is the diameter of the graph. Moreover, we present a simple distributed heuristic algorithm and conduct an extensive simulation study showing that our heuristic outperforms previously known approaches for the problem.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  1. Abu-Khzam, F., Markarian, C.: A degree-based heuristic for strongly connected dominating-absorbent sets in wireless ad-hoc networks. In: Innovations in Information Technology, pp. 200–204 (2012)

  2. Markarian, C., Meyer auf der Heide, F., Schubert, M.: A distributed approximation algorithm for strongly connected dominating-absorbent sets in asymmetric wireless ad-hoc networks. In: ALGOSENSORS, pp. 217–227 (2013)

  3. Cardei, M., Cheng, X., Cheng, X., Zhu Du, D.: Connected domination in multihop ad-hoc wireless networks. In: International Conference on Computer Science and Informatics, pp. 251–255 (2002)

  4. Wu, J.: Extended dominating-set-based routing in ad-hoc wireless networks with unidirectional links. IEEE Trans. Parallel Distrib. Syst. 13(9), 866–881 (2004)

    MathSciNet  Google Scholar 

  5. Wu, J., Dai, F., Gao, M., Stojmenovic, I.: On calculating power-aware connected dominating sets for efficient routing in ad-hoc wireless networks. IEEE Journal of Communications and Networks 4(1), 59–70 (2002)

    Article  Google Scholar 

  6. Das, B., Bharghavan, V.: Routing in ad-hoc networks using minimum connected dominating sets. In: International Conference on Communications, pp. 376–380 (1997)

  7. Das, B., Sivakumar, R., Bharghavan, V.: Routing in ad-hoc networks using a spine. In: International Conference on Computers and Communication Networks, pp. 34–39 (1997)

  8. Dai, F., Wu, J.: An Extended Localized Algorithm for Connected Dominating Set Formation in Ad-hoc Wireless Networks. IEEE Trans. Parallel Distrib. Syst. 15 (10), 908–920 (2004)

    Article  Google Scholar 

  9. Schneider, J., Wattenhofer, R.: A log-star distributed maximal independent set algorithm for growth-bounded graphs. In: Principles of Distributed Computing, pp. 35–44 (2008)

  10. Clark, B., Colbourn, C., Johnson, D.: Unit disk graphs. Discret. Math. 86, 165–177 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  11. Lenzen, C., Wattenhofer, R.: Leveraging Linial’s locality limit. Distrib. Comput. 5218, 394–407 (2008)

    MATH  Google Scholar 

  12. Yadav, A.K., Yadav, R.S., Singh, R., Singh, A.K.: Connected dominating set for wireless ad hoc networks: a survey. International Journal of Engineering Systems Modelling and Simulation 7(1), 22–34 (2015)

    Article  MathSciNet  Google Scholar 

  13. Yu, J., Wang, N., Wang, G., Yu, D.: Connected dominating sets in wireless ad hoc and sensor networks – a comprehensive survey. Comput. Commun. 36(2), 121–134 (2013)

    Article  Google Scholar 

  14. Guha, S., Khuller, S.: Approximation algorithms for connected dominating sets. Algoritmica 20(4), 374–387 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  15. Min, M., Du, H., Jia, X., Huang, C.X., Huang, S.C.H., Wu, W.: Improving construction for connected dominating set with steiner tree in wireless sensor networks. J. Glob. Optim. 35(1), 111–119 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  16. Butenko, S., Cheng, X., Obviera, C.A., Pardalos, P.: A new heuristic for the minimum connected dominating set problem on ad-hoc wireless networks. In: Recent Developments in Cooperative Control and Optimization, pp. 61–73 (2004)

  17. Alzoubi, K., Wan, R.-J., Frieder, O.: New distributed algorithm for connected dominating set in wireless ad-hoc networks. In: International Conference on System Sciences, pp. 3849–3855 (2002)

  18. Alzoubi, K.M., Wan, R.-J., Frieder, O.: Message-optimal connected dominating sets in mobile ad-hoc networks. In: ACM International Symposium on Mobile Ad-Hoc Networking and Computing, pp. 157–164 (2002)

  19. Czyzowicz, J., Dobrev, S., Fevens, T., González-Aguilar, H., Kranakis, E., Opatrny, J., Urrutia, J.: Local algorithms for dominating and connected dominating sets of unit disk graphs with location aware nodes. In: Latin American Symposium on Theoretical Informatics, vol. 4957, pp. 158–169 (2008)

  20. Funke, S., Kesselman, A., Meyer, U., Segal, M.: A simple improved distributed algorithm for minimum CDS in unit disk graphs. ACM Transactions on Sensor Networks 2(3), 444–453 (2006)

    Article  Google Scholar 

  21. Han, B.: Zone-based virtual backbone formation in wireless ad-hoc networks. Ad Hoc Netw. 7(l), 183–200 (2009)

    Article  Google Scholar 

  22. Wu, J., Li, H.: On calculating connected dominating set for efficient routing in ad-hoc wireless networks. In: International Workshop on Discrete Algorithms and Methods for Mobile Computing and Communications, pp. 7–14 (1999)

  23. Wu, J., Gao, M., Stojmenovic, I.: On calculating power-aware connected dominating sets for efficient routing in ad-hoc wireless networks. In: International Conference on Parallel Processing, pp. 346–356 (2001)

  24. Kassaei, H., Mehrandish, M., Narayanan, L., Opatrny, J.: A new local algorithm for backbone formation in ad-hoc networks. In: ACM Symposium on Performance Evaluation of Wireless Ad-Hoc, Sensor, and Ubiquitous Networks, pp. 49–57 (2009)

  25. Yu, J., Jia, L., Yu, D., Li, G., Cheng, X.: Minimum connected dominating set construction in wireless networks under the beeping model. In: Computer Communications (INFOCOM), pp. 972–980 (2015)

  26. Chaturvedi, O., Kaur, P., Ahuja, N., Prakash, T.: Improved algorithms for construction of connected dominating set in MANETs. In: Cloud System and Big Data Engineering (Confluence), pp. 559–564 (2016)

  27. Tang, W., Li, J., He, Q.: A highly efficient distributed algorithm for constructing CDS in wireless ad hoc networks with partial neighborhood notification. In: International Conference on Modelling and Simulation, pp. 549–553 (2015)

  28. Thai, M., Wang, F., Liu, D., Zhu, S., Du, D.: Connected dominating sets in wireless networks with different transmission ranges. Mob. Commun. 6(7), 721–730 (2007)

    Google Scholar 

  29. Raei, H., Fathi, M., Akhhlaghi, A., Ahmadipoor, B.: A new distributed algorithm for virtual backbone in wireless sensor networks with different transmission ranges. In: Computer Systems and Applications, pp. 983–988 (2009)

  30. Raei, H., Sarram, M., Salimi, B., Adibnya, F.: Energy-aware distributed algorithm for virtual backbone in wireless sensor networks. In: Innovations in Information Technology, pp. 435–439 (2008)

  31. Wu, J.: An extended dominating-set-based routing in ad hoc wireless networks with unidirectional links. IEEE Trans. Parallel Distrib. Syst. 13(9), 866–881 (2002)

    Article  Google Scholar 

  32. Park, M.A., Willson, J., Wang, C., Thai, M., Wu, W., Farago, A.: A dominating and absorbent set in a wireless adhoc network with different transmission ranges. In: Mobile Ad hoc Networking and Computing, pp. 22–31 (2007)

  33. Kassaei, H., Narayanan, L.: A new algorithm for backbone formation in ad hoc wireless networks of nodes with different transmission ranges. In: Wireless and Mobile Computing, pp. 83–90 (2010)

  34. Zhang, Z., Wu, W., Wu, L., Li, Y., Chen, Z.: Strongly connected dominating and absorbing set in directed disk graph. International Journal of Sensor Networks 19(2), 69–77 (2015)

    Article  Google Scholar 

  35. Li, D., Duc, H., Wan, P.: Construction of strongly connected dominating sets in asymmetric multihop wireless networks. Theor. Comput. Sci. 410, 661–669 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  36. Alon, N., Moshkovitz, D., Safra, S.: Algorithmic construction of sets for k-restrictions. ACM Trans. Algorithms 2(2), 153–177 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  37. Luby, M.: A simple parallel algorithm for the maximal independent set problem. SIAM J. Comput. 15(4), 1036–1053 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  38. Thai, M., Wang, F., Liu, D., Zhu, S., Du, D.: Connected dominating sets in wireless networks with different transmission ranges. Mobile Computing 6(7), 721–730 (2007)

    Article  Google Scholar 

  39. Ahn, N., Park, S.: An optimization algorithm for the minimum k-connected m-dominating set problem in wireless sensor networks. Wirel. Netw 21(3), 783–792 (2015)

    Article  Google Scholar 

  40. Tiwari, R., Thai, M.T.: On enhancing fault tolerance of virtual backbone in a wireless sensor network with unidirectional links sensors. In: Theory, Algorithms, and Applications, pp. 3–18 (2011)

  41. Tiwari, R., Mishra, T., Li, Y.: k-strongly connected dominating and absorbing set in wireless ad hoc networks with unidirectional links. In: Wireless Algorithm, Systems and Applications, pp. 103–112 (2007)

  42. Alon, N., Awerbuch, B., Azar, Y., Buchbinder, N., Naor, J.: The online set cover problem. In: ACM Symposium on the Theory of Computation, pp. 100–105 (2003)

  43. Caragiannisa, I., Fishkinb, A.V., Kaklamanisa, C., Papaioannoua, E.: Randomized online algorithms and lower bounds for computing large independent sets in disk graphs. Symposium on Mathematical Foundations of Computer Science 155 (2), 119–136 (2007)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, Mathematics, Lebanese American University, Beirut, Lebanon

    Faisal N. Abu-Khzam

  2. Heinz Nixdorf Institute & Computer Science Department, University of Paderborn, 33102, Paderborn, Germany

    Christine Markarian & Friedhelm Meyer auf der Heide

  3. Department of Mathematics, University of Paderborn, 33102, Paderborn, Germany

    Michael Schubert

Authors
  1. Faisal N. Abu-Khzam
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Christine Markarian
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Friedhelm Meyer auf der Heide
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Michael Schubert
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Christine Markarian.

Additional information

Based on ideas suggested and partially developed in two conference papers [1] and [2]. This work was partially supported by the German Research Foundation (DFG) within the Collaborative Research Center ‘On-The-Fly Computing’ (SFB 901) and the Federal Ministry of Education and Research (BMBF) as part of the project ‘Resilience by Spontaneous Volunteers Networks for Coping with Emergencies and Disaster’ (RESIBES), (grant no 13N13955 to 13N13957).

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Abu-Khzam, F.N., Markarian, C., Heide, F.M.a.d. et al. Approximation and Heuristic Algorithms for Computing Backbones in Asymmetric Ad-hoc Networks. Theory Comput Syst 62, 1673–1689 (2018). https://doi.org/10.1007/s00224-017-9836-z

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00224-017-9836-z

Keywords

Search

Navigation