Skip to main content
SpringerLink
Log in

Shared Multicast Trees in Ad Hoc Wireless Networks

  • Conference paper
  • First Online:
Combinatorial Optimization (ISCO 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9849))

Included in the following conference series:

  • 1020 Accesses

Abstract

This paper addresses a problem of shared multicast trees (SMT), which extends a recently studied problem of shared broadcast trees (SBT). In SBT, a common optimal tree for a given set of nodes allowing broadcasting from any node to the rest of the group is searched. In SMT, also nodes that neither initiate any transmission, nor act as destinations are considered. Their purpose is exclusively to relay messages between nodes. The optimization criterion is to minimize the energy consumption. The present work introduces this generalization and devises solution methods. We model the problem as an integer linear program (ILP), in order to compute the exact solution. However, the size of instances solvable by ILP is significantly limited. Therefore, we also focus on inexact methods allowing us to process larger instances. We design a fast greedy method and compare its performance with adaptations of algorithms solving related problems. Numerical experiments reveal that the presented greedy method produces trees of lower energy than alternative approaches, and the solutions are close to the optimum.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Althaus, E., Calinescu, G., Mandoiu, I.I., Prasad, S., Tchervenski, N., Zelikovsky, A.: Power efficient range assignment in ad-hoc wireless networks. Wirel. Commun. Networking 3, 1889–1894 (2003)

    Google Scholar 

  2. Ambühl, C.: An optimal bound for the MST algorithm to compute energy efficient broadcast trees in wireless networks. In: Caires, L., Italiano, G.F., Monteiro, L., Palamidessi, C., Yung, M. (eds.) ICALP 2005. LNCS, vol. 3580, pp. 1139–1150. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  3. Bauer, J., Haugland, D., Yuan, D.: New results on the time complexity and approximation ratio of the broadcast incremental power algorithm. Inf. Process. Lett. 109(12), 615–619 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  4. Bein, D., Zheng, S.Q.: Energy efficient all-to-all broadcast in all-wireless networks. Inf. Sci. 180(10), 1781–1792 (2010)

    Article  MathSciNet  Google Scholar 

  5. Bhukya, W.N., Singh, A.: An effective heuristic for construction of all-to-all minimum power broadcast trees in wireless networks. In: Advances in Computing, Communications and Informatics, pp. 74–79 (2014)

    Google Scholar 

  6. Blough, D.M., Leoncini, M., Resta, G., Santi, P.: On the symmetric range assignment problem in wireless ad hoc networks. In: Proceedings of the IFIP 17th World Computer Congress - TC1 Stream / 2nd IFIP International Conference on Theoretical Computer Science: Foundations of Information Technology in the Era of Networking and Mobile Computing, pp. 71–82 (2002)

    Google Scholar 

  7. Clementi, E.F., Penna, P., Silvestri, R.: On the power assignment problem in radio networks. Mob. Netw. Appl. Discrete Algorithms Methods Mob. Comput. Commun. 9(2), 125–140 (2004)

    MATH  Google Scholar 

  8. Das, A.K., Marks, R.J., El-sharkawi, M.: Minimum power broadcast trees for wireless networks: integer programming formulations. In: The 22nd Annual Joint Conference of the IEEE Computer and Communications Societies, pp. 245–248 (2003)

    Google Scholar 

  9. Das, A.K., Marks II, R.J., El-Sharkawi, M., Arabshahi, P., Gray, A.: Optimization methods for minimum power bidirectional topology construction in wireless networks with sectored antennas. In: Global Telecommunications Conference, vol. 6, pp. 3962–3968 (2004)

    Google Scholar 

  10. Das, A.K., Marks, R.J., El-sharkawi, M., Arabshahi, P., Gray, A.: r-Shrink: a heuristic for improving minimum power broadcast trees in wireless networks. In: Proceedings of the IEEE GLOBECOM 2003, vol. 1, pp. 523–527 (2003)

    Google Scholar 

  11. Das, A.K., Marks, R.J., El-sharkawi, M., Arabshahi, P., Gray, A.: e-Merge: A heuristic for improving minimum power broadcast trees in wireless networks, Technical report. University of Washington, Department of Electrical Engineering (2003)

    Google Scholar 

  12. Haugland, D., Yuan, D.: Wireless Network Design: Optimization Models and Solution Procedures. International Series in Operations Research & Management Science, vol. 158. Springer, New York (2011). pp. 219–246

    Book  Google Scholar 

  13. Liang, W.: Constructing minimum-energy broadcast trees in wireless ad hoc networks. In: Proceedings of the 3rd ACM International Symposium on Mobile Ad Hoc Networking & Computing, pp. 112–122 (2002)

    Google Scholar 

  14. Hwang, F.K., Richards, D.S., Winter, P.: The Steiner Tree Problem. Annals of Discrete Mathematics. Elsevier Science, Netherlands (1992)

    MATH  Google Scholar 

  15. Montemanni, R., Gambardella, L.M.: Exact algorithms for the minimum power symmetric connectivity problem in wireless networks. Comput. Oper. Res. 32(11), 2891–2904 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  16. Papadimitriou, I., Georgiadis, L.: Minimum-energy broadcasting in multi-hop wireless networks using a single broadcast tree. Mob. Networks Appl. 11(3), 361–375 (2006)

    Article  Google Scholar 

  17. Wan, P., Clinescu, G., Yi, C.: Minimum-power multicast routing in static ad hocwireless networks. IEEE/ACM Trans. Networking (TON) 12(3), 507–514 (2004)

    Article  Google Scholar 

  18. Wieselthier, J.E., Nguyen, G.D., Ephremides, A.: On the construction of energy-efficient broadcast and multicast trees in wireless networks. In: Proceedings of the Nineteenth Annual Joint Conference of the IEEE Computer and Communications Societies, vol. 2, pp. 585–594 (2000)

    Google Scholar 

  19. Yuan, D., Haugland, D.: Dual decomposition for computational optimization of minimum-power shared broadcast tree in wireless networks. IEEE Trans. Mob. Comput. 12(11), 2008–2019 (2012)

    Article  Google Scholar 

  20. IBM ILOG CPLEX V12.1 User’s Manual for CPLEX (2009)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Bergen, Bergen, Norway

    Marika Ivanova

Authors
  1. Marika Ivanova
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Marika Ivanova .

Editor information

Editors and Affiliations

  1. University of Salerno , Fisciano, Italy

    Raffaele Cerulli

  2. Kyoto University , Kyoto, Japan

    Satoru Fujishige

  3. LAMSADE, Université Paris-Dauphine , Paris , France

    A. Ridha Mahjoub

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this paper

Cite this paper

Ivanova, M. (2016). Shared Multicast Trees in Ad Hoc Wireless Networks. In: Cerulli, R., Fujishige, S., Mahjoub, A. (eds) Combinatorial Optimization. ISCO 2016. Lecture Notes in Computer Science(), vol 9849. Springer, Cham. https://doi.org/10.1007/978-3-319-45587-7_24

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-45587-7_24

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-45586-0

  • Online ISBN: 978-3-319-45587-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation