Improved Approximation Bounds for Maximum Lifetime Problems in Wireless Ad-Hoc Network

  • Sang Hyuk Lee
  • Tomasz Radzik
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7363)


A wireless ad-hoc network consists of a number of wireless devices (nodes), that communicate with each other within the network using their built-in radio transceivers. The nodes are in general battery-powered, thus their lifetime is limited. Therefore, algorithms for maximizing the network lifetime are of great interest. In this paper we consider the Rooted Maximum Network Lifetime (RMNL) problems: given a network N and a node r, the objective is to find a maximum-size collection of routing trees rooted at the node r for a specified communication pattern. The number of such trees represents the total number of communication rounds executed before the first node in the network dies due to battery depletion. We consider two communication patterns, broadcast and convergecast.

We follow the approach used by Nutov and Segal in [15], who developed polynomial time approximation algorithms with constant approximation ratios for the broadcast and convergecast RMNL problems. Our analysis of their algorithms leads to better approximation ratios than the ratios derived in [15]. In particular, we show a 1/7 approximation ratio for the multiple topology convergecast RMNL problem, improving the previous ratio of 1/31.


Network Lifetime Broadcast Convergecast Approximation algorithm Wireless ad-hoc network 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bhalgat, A., Hariharan, R., Kavitha, T., Panigrahi, D.: Fast edge splitting and edmonds’ arborescence construction for unweighted graphs. In: SODA, pp. 455–464 (2008)Google Scholar
  2. 2.
    Deng, G., Gupta, S.K.S.: Maximizing broadcast tree lifetime in wireless ad hoc networks. In: GLOBECOM (2006)Google Scholar
  3. 3.
    Edmonds, J.: Edge-disjoint branchings. In: Rustin, B. (ed.) Combinatorial Algorithms, pp. 91–96. Academic Press (1973)Google Scholar
  4. 4.
    Elkin, M., Lando, Y., Nutov, Z., Segal, M., Shpungin, H.: Novel algorithms for the network lifetime problem in wireless settings. Wireless Networks 17(2), 397–410 (2011)CrossRefGoogle Scholar
  5. 5.
    Fürer, M., Raghavachari, B.: Approximating the minimum-degree steiner tree to within one of optimal. J. Algorithms 17(3), 409–423 (1994)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Gabow, H.N., Manu, K.S.: Packing algorithms for arborescences (and spanning trees) in capacitated graphs. Math. Program. 82, 83–109 (1998)MathSciNetzbMATHGoogle Scholar
  7. 7.
    Kalpakis, K., Dasgupta, K., Namjoshi, P.: Efficient algorithms for maximum lifetime data gathering and aggregation in wireless sensor networks. Computer Networks 42(6), 697–716 (2003)zbMATHCrossRefGoogle Scholar
  8. 8.
    Kang, I., Poovendran, R.: Maximizing static network lifetime of wireless broadcast adhoc networks. In: IEEE International Conference on Communications, ICC 2003, pp. 2256–2261 (2003)Google Scholar
  9. 9.
    Kang, I., Poovendran, R.: Maximizing network lifetime of broadcasting over wireless stationary ad hoc networks. MONET 10(6), 879–896 (2005)Google Scholar
  10. 10.
    Liang, W., Liu, Y.: Online data gathering for maximizing network lifetime in sensor networks. IEEE Trans. Mob. Comput. 6(1), 2–11 (2007)CrossRefGoogle Scholar
  11. 11.
    Lin, H.C., Li, F.J., Wang, K.Y.: Constructing maximum-lifetime data gathering trees in sensor networks with data aggregation. In: ICC, pp. 1–6 (2010)Google Scholar
  12. 12.
    Maric, I., Yates, R.D.: Cooperative multicast for maximum network lifetime. IEEE Journal on Selected Areas in Communications 23(1), 127–135 (2005)CrossRefGoogle Scholar
  13. 13.
    Nutov, Z.: Approximating directed weighted-degree constrained networks. In: APPROX-RANDOM, pp. 219–232 (2008)Google Scholar
  14. 14.
    Nutov, Z.: Approximating maximum integral flows in wireless sensor networks via weighted-degree constrained k-flows. In: DIALM-POMC, pp. 29–34 (2008)Google Scholar
  15. 15.
    Nutov, Z., Segal, M.: Improved Approximation Algorithms for Maximum Lifetime Problems in Wireless Networks. In: Dolev, S. (ed.) ALGOSENSORS 2009. LNCS, vol. 5804, pp. 41–51. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  16. 16.
    Orda, A., Yassour, B.A.: Maximum-lifetime routing algorithms for networks with omnidirectional and directional antennas. In: MobiHoc, pp. 426–437 (2005)Google Scholar
  17. 17.
    Park, J., Sahni, S.: Maximum lifetime broadcasting in wireless networks. In: AICCSA, p. 8. IEEE Computer Society (2005)Google Scholar
  18. 18.
    Segal, M.: Fast algorithm for multicast and data gathering in wireless networks. Inf. Process. Lett. 107(1), 29–33 (2008)zbMATHCrossRefGoogle Scholar
  19. 19.
    Stanford, J., Tongngam, S.: Approximation algorithm for maximum lifetime in wireless sensor networks with data aggregation. In: SNPD, pp. 273–277 (2006)Google Scholar
  20. 20.
    Wu, Y., Fahmy, S., Shroff, N.B.: On the construction of a maximum-lifetime data gathering tree in sensor networks: Np-completeness and approximation algorithm. In: INFOCOM, pp. 356–360 (2008)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Sang Hyuk Lee
    • 1
  • Tomasz Radzik
    • 1
  1. 1.Department of InformaticsKing’s College LondonLondonUK

Personalised recommendations