Abstract
Given a set S of points (stations) located in the d-dim. Euclidean space and a rootb ∈S, 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.
Supported by the European Union under the Integrated Project IST-15964 AEOLUS (“Algorithmic Principles for Building Efficient Overlay Computers”).
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Alfandari, L., Paschos, V.T.: Approximating minimum spanning tree of depth 2. Intl. Trans. In Op. Res. 6, 607–622 (1999)
Alon, N., Spencer, J.: The probabilistic method. Wiley, Chichester (1992)
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)
Chlebus, B., Gasienec, L., Gibbons, A., Pelc, A., Rytter, W.: Deterministic broadcasting in unknown radio networks. In: Proc. of 11th ACM SODA (2000)
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)
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)
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)
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)
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)
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)
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)
Gouveia, L.: Multicommodity flow models for spanning trees with hop constraints. European Journal of Operational Research 95, 178–190 (1996)
Guha, S., Khuller, S.: Greedy strikes back: Improved facility location algorithms. Journal of Algorithms 31, 228–248 (1999)
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)
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)
Kirousis, L.M., Kranakis, E., Krizanc, D., Pelc, A.: Power Consumption in Packet Radio Networks. Theoretical Computer Science 243, 289–305 (2000)
Kortsarz, G., Peleg, D.: Approximating the weight of shallow Steiner trees. Discrete Applied Mathematics 93, 265–285 (1999)
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)
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)
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)
Pahlavan, K., Levesque, A.: Wireless Information Networks. Wiley-Interscience, Chichester (1995)
Ramanathan, S., Lloyd, E.: Scheduling Broadcasts in multi-hop radio networks. IEEE/ACM Trans. on Networking 1 (1993)
Ramanathan, R., Hain, R.: Topology Control of Multihop Wireless Networks Using Transmit Power Adjustment. In: Proc of IEEE INFOCOM, pp. 404–413 (2000)
Ramaswami, R., Parhi, K.: Distributed scheduling of broadcasts in radio networks. In: Proc of IEEE INFOCOM (1989)
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)
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)
Voss, S.: The steiner tree problem with hop constraint. Annals of Operations Research 86, 321–345 (1999)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Clementi, A.E.F., Di Ianni, M., Lauria, M., Monti, A., Rossi, G., Silvestri, R. (2006). A Distributed Protocol for the Bounded-Hops Converge-Cast in Ad-Hoc Networks. In: Kunz, T., Ravi, S.S. (eds) Ad-Hoc, Mobile, and Wireless Networks. ADHOC-NOW 2006. Lecture Notes in Computer Science, vol 4104. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11814764_7
Download citation
DOI: https://doi.org/10.1007/11814764_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-37246-2
Online ISBN: 978-3-540-37248-6
eBook Packages: Computer ScienceComputer Science (R0)