A Distributed Protocol for the Bounded-Hops Converge-Cast in Ad-Hoc Networks

  • Andrea E. F. Clementi
  • Miriam Di Ianni
  • Massimo Lauria
  • Angelo Monti
  • Gianluca Rossi
  • Riccardo Silvestri
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4104)


Given a set S of points (stations) located in the d-dim. Euclidean space and a rootbS, the h -hops Convergecast problem asks to find for a minimal energy-cost range assignment which allows to perform the converge-cast primitive (i.e. node accumulation) towards b in at most h hops. For this problem no polynomial time algorithm is known even for h = 2.

The main goal of this work is the design of an efficient distributed heuristic (i.e. protocol) and the analysis (both theoretical and experimental) of its expected solution cost. In particular, we introduce an efficient parameterized randomized protocol for h -hops Convergecast and we analyze it on random instances created by placing n points uniformly at random in a d-cube of side length L. We prove that for h = 2, its expected approximation ratio is bounded by some constant factor. Finally, for h = 3,..., 8, we provide a wide experimental study showing that our protocol has very good performances when compared with previously introduced (centralized) heuristics.


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  1. 1.
    Alfandari, L., Paschos, V.T.: Approximating minimum spanning tree of depth 2. Intl. Trans. In Op. Res. 6, 607–622 (1999)CrossRefMathSciNetGoogle Scholar
  2. 2.
    Alon, N., Spencer, J.: The probabilistic method. Wiley, Chichester (1992)zbMATHGoogle Scholar
  3. 3.
    Arora, S., Raghavan, P., Rao, S.: Approximation schemes for Euclidean k-medians and related problems. In: Proc. 30-th ACM Symposium on Theory of Computing, pp. 106–113 (1998)Google Scholar
  4. 4.
    Chlebus, B., Gasienec, L., Gibbons, A., Pelc, A., Rytter, W.: Deterministic broadcasting in unknown radio networks. In: Proc. of 11th ACM SODA (2000)Google Scholar
  5. 5.
    Chudak, F.A., Williamson, D.P.: Improved approximation algorithms for capacitated facility location problems. In: Cornuéjols, G., Burkard, R.E., Woeginger, G.J. (eds.) IPCO 1999. LNCS, vol. 1610, p. 99. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  6. 6.
    Clementi, A.E.F., Penna, P., Silvestri, R.: On the Power Assignment Problem in Radio Networks. Mobile Networks and Applications (MONET) 9, 125–140 (2004)CrossRefGoogle Scholar
  7. 7.
    Clementi, A.E.F., Huiban, G., Penna, P., Rossi, G., Verhoeven, Y.: Some Recent Theoretical Advances and Open Questions on Energy Consumption in Static Ad-Hoc in Wireless Networks. In: Proc. of the 3rd Workshop ARACNE, Carleton Scientific (2002)Google Scholar
  8. 8.
    Clementi, A.E.F., Di Ianni, M., Monti, A., Rossi, G., Silvestri, R.: Experimental Analysis of Practically Efficient Algorithms for Bounded-Hop Accumulation in Ad-Hoc Wireless Networks. In: Proc. of the IEEE IPDPS-WMAN (2005)Google Scholar
  9. 9.
    Clementi, A.E.F., Di Ianni, M., Monti, A., Lauria, M., Rossi, G., Silvestri, R.: Divide and conquer is almost optimal for the bounded-hop MST problem on random euclidean instances. In: Pelc, A., Raynal, M. (eds.) SIROCCO 2005. LNCS, vol. 3499, pp. 89–98. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  10. 10.
    Ephremides, A., Nguyen, G.D., Wieselthier, J.E.: On the Construction of Energy-Efficient Broadcast and Multicast Trees in Wireless Networks. In: Proc. of the 19th INFOCOM, pp. 585–594 (2000)Google Scholar
  11. 11.
    Gouveia, L.: Using the Miller-Tucker-Zemlin constraints to formulate a minimal spanning tree problem with hop constraints. Computers and Operations Research 22, 959–970 (1995)zbMATHCrossRefGoogle Scholar
  12. 12.
    Gouveia, L.: Multicommodity flow models for spanning trees with hop constraints. European Journal of Operational Research 95, 178–190 (1996)zbMATHCrossRefGoogle Scholar
  13. 13.
    Guha, S., Khuller, S.: Greedy strikes back: Improved facility location algorithms. Journal of Algorithms 31, 228–248 (1999)zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Gouveia, L., Requejo, C.: A new relaxation approach for the hop-constrain minimum spanning tree problem. European Journal of Operational Research 132, 539–552 (2001)zbMATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Kesselman, A., Kowalski, D.R.: Fast Distributed Algorithm for Convergecast in Ad Hoc Geometric Radio Networks. In: Proc. of the 2nd International Conference on Wireless on Demand Network Systems and Service, pp. 119–124 (2005)Google Scholar
  16. 16.
    Kirousis, L.M., Kranakis, E., Krizanc, D., Pelc, A.: Power Consumption in Packet Radio Networks. Theoretical Computer Science 243, 289–305 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Kortsarz, G., Peleg, D.: Approximating the weight of shallow Steiner trees. Discrete Applied Mathematics 93, 265–285 (1999)zbMATHCrossRefMathSciNetGoogle Scholar
  18. 18.
    Korupolu, M.R., Plaxton, C.G., Rajaraman, R.: Analysis of a Local Search Heuristic for Facility Location Problems. In: Proc. of the 9-th annual ACM-SIAM symposium on Discrete algorithms, pp. 1–10 (1998)Google Scholar
  19. 19.
    Lloyd, E.L., Liu, R., Marathe, M.V., Ramanathan, R., Ravi, S.S.: Algorithmic Aspects of Topology Control Problems for Ad Hoc Networks. Mobile Networks and Applications 10, 19–34 (2005)CrossRefzbMATHGoogle Scholar
  20. 20.
    Mahdian, M., Ye, Y., Zhang, J.: A 1.52-approximation algorithm for the uncapacitated facility location problem. In: Jansen, K., Leonardi, S., Vazirani, V.V. (eds.) APPROX 2002. LNCS, vol. 2462, pp. 229–242. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  21. 21.
    Pahlavan, K., Levesque, A.: Wireless Information Networks. Wiley-Interscience, Chichester (1995)Google Scholar
  22. 22.
    Ramanathan, S., Lloyd, E.: Scheduling Broadcasts in multi-hop radio networks. IEEE/ACM Trans. on Networking 1 (1993)Google Scholar
  23. 23.
    Ramanathan, R., Hain, R.: Topology Control of Multihop Wireless Networks Using Transmit Power Adjustment. In: Proc of IEEE INFOCOM, pp. 404–413 (2000)Google Scholar
  24. 24.
    Ramaswami, R., Parhi, K.: Distributed scheduling of broadcasts in radio networks. In: Proc of IEEE INFOCOM (1989)Google Scholar
  25. 25.
    Raidl, G.R., Julstrom, B.A.: Greedy Heuristics and an Evolutionary Algorithm for the Bounded-Diameter Minimum Spanning Tree Problem. In: Proc. of the 2003 ACM symposium on Applied computing, pp. 747–752 (2003)Google Scholar
  26. 26.
    Shmoys, D.B., Tardos, E., Aardal, K.: Approximation algorithms for facility location problems. In: Proc. of the 29-th Annual ACM Symposium on Theory of Computing (STOC), pp. 265–274 (1997)Google Scholar
  27. 27.
    Voss, S.: The steiner tree problem with hop constraint. Annals of Operations Research 86, 321–345 (1999)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Andrea E. F. Clementi
    • 1
  • Miriam Di Ianni
    • 1
  • Massimo Lauria
    • 2
  • Angelo Monti
    • 2
  • Gianluca Rossi
    • 1
  • Riccardo Silvestri
    • 2
  1. 1.Dipartimento di MatematicaUniversità degli Studi di Roma “Tor Vergata” 
  2. 2.Dipartimento di InformaticaUniversità degli Studi di Roma “La Sapienza” 

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