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Compact Integer Programming Models for Power-optimal Trees in Ad Hoc Wireless Networks

  • Dag Haugland
  • Di Yuan
Chapter
Part of the International Series in Operations Research & Management Science book series (ISOR, volume 158)

Abstract

This chapter examines two types of optimization problems of minimizing the total transmission power required to satisfy some connectivity requirement for a group of nodes in ad hoc wireless networks. The first problem type is broadcast and multicast of messages from a source node to the rest of the group. The second problem type, also known as range assignment, amounts to forming a strongly connected subgraph containing all nodes of the group by bi-directional links. Optimal solutions to these problems are characterized by trees or arborescences. As a consequence of power minimization in a wireless transmission environment, the structural properties of these optimal trees and arborescences differ significantly from the classical ones. We discuss compact integer programming models for both problem types. In addition to reviewing models based on network flows, we develop a new compact model for range assignment. We provide theoretical analysis of how the models relate to each other in the strengths of their linear programming (LP) relaxations. Experimental results are provided to illustrate the performance of the models in bounding and in approaching integer optimality. The new compact model for range assignment turns out to be very competitive in both aspects.

Keywords

Wireless Network Minimum Span Tree Steiner Tree Valid Inequality Linear Programming Relaxation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Aggélou, G.N.: An integrated platform for ad hoc GSM cellular communications. In Ilyas. M. (ed.) The Handbook of Ad hoc Wireless Networks, pp. 189–203. CRC press (2002).Google Scholar
  2. 2.
    Ahuja, R.K., Magnanti, T.L., Orlin, J.B.: Network Flows: Theory, Algorithms, and Applications. Prentice Hall, Upper Saddle River, NJ (1993)Google Scholar
  3. 3.
    Akyildiz, I. F., Su, W., Sankarasubramaniam, Y., Cayirci, E.: Wireless sensor networks: a survey. Computer Networks 38, 393–422 (2002).CrossRefGoogle Scholar
  4. 4.
    Akyildiz, I. F., Wang, X., Wang W.: Wireless sensor networks: a survey. Computer Networks 47, 445–487 (2005).CrossRefGoogle Scholar
  5. 5.
    Althaus, E., Căalinescu, G., Mandoiu, I., Prasad, S., Tchervenski, N., Zelikovsky, A.: Power efficient range assignment in ad-hoc wireless networks. In: Proceedings of IEEE WCNC’03, pp. 1889–1994 (2003).Google Scholar
  6. 6.
    Althaus, E., Călinescu, G., Mandoiu, I., Prasad, S., Tchervenski, N., Zelikovsky, A.: Power efficient range assignment in ad-hoc wireless networks.Wireless Networks 12, 287–299 (2006).Google Scholar
  7. 7.
    Altinkemer, K., Salman, F.S., Bellur, P.: Solving the minimum energy broadcasting problem in ad hoc wireless networks by integer programming. In: Proceedings of the second workshop on modeling and optimization in mobile, ad hoc, and wireless Networks (WiOpt’04), pp. 48–54 (2004).Google Scholar
  8. 8.
    Ambühl, C.: An optimal bound for the MST algorithm to compute energy efficient broadcast trees in wireless networks. In: Lecture Notes in Computer Science 3580, pp. 1139–1150 (2005).CrossRefGoogle Scholar
  9. 9.
    Ambühl, C., Clementi, A., Ianni, M.D., Rossi, G., Monti, A., Silvestri, R.: The range assignment problem in non-homogeneous static ad-hoc networks. In: Proceedings of the IEEE 18th International Parallel and Distributed Processing Symposium (2004).Google Scholar
  10. 10.
    Bauer, J., Haugland, D., Yuan, D.: Analysis and computational study of several integer programming formulations for minimum-energy multicasting in wireless ad hoc networks. Networks 52, 57–68 (2008).CrossRefGoogle Scholar
  11. 11.
    Bauer, J., Haugland, D., Yuan, D.: New results on the time complexity and approximation ratio of the broadcast incremental power algorithm. Information Processing Letters 109, 615–619 (2009).CrossRefGoogle Scholar
  12. 12.
    Bauer, J., Haugland, D., Yuan, D.: A fast local search methods for minimum energy broadcast in wireless ad hoc networks. Operations Research Letters 37, 75–79 (2009).CrossRefGoogle Scholar
  13. 13.
    Baumann, F., Buchheim, C. (2009). Compact and extended formulations for range assignment problems. Zentrum f¨ur Angewandte Informatik Köln, Lehrstuhl Jünger, Germany. http://www.zaik.uni-koeln.de/ paper/unzip.html?file=zaik2009-582.pdf Cited 23 July 2009.
  14. 14.
    Căgalj, M., Hubaux, J.-P., Enz, C.: Minimum-energy broadcast in all-wireless networks: Npcompleteness and distribution issues. In: Proceedings of ACM MobiCom’02, pp. 172–182 (2002).Google Scholar
  15. 15.
    Căgalj, M., Hubaux, J.-P., Enc, C.: Energy-efficient broadcasting in all-wireless networks, Mobile Networks and Applications 11, 177–188 (2005).Google Scholar
  16. 16.
    Caragiannis, I., Kaklamanis, C., Kanellopoulos, P.: Power consumption problems in ad-hoc wireless networks. In Lecture Notes in Computer Science 2909, pp. 252–255 (2004).CrossRefGoogle Scholar
  17. 17.
    Calinescu, G., Kapoor, S., Sarwat, M.: Bounded-hops power assignment in ad hoc wireless networks. Discrete Applied Mathematics 154, 1358–1371 (2006).CrossRefGoogle Scholar
  18. 18.
    Chu, T., Nikoladis, I.: Energy efficient broadcast in mobile ad hoc networks. In: Proceedings of the 1st International Conference on Ad-Hoc Networks and Wireless (ADHOC-NOW), pp. 177–190 (2002).Google Scholar
  19. 19.
    Clementi, A., Penna, P., Silvestri, R.: Hardness results for the power range assignment problem in packet radio networks. In: Lecture Notes in Computer Science 1671, pp. 197–208. Springer (1999).Google Scholar
  20. 20.
    Clementi, A., Penna, P., Silvestri, R.: The power range assignment problem in radio networks on the plane. In: Lecture Notes in Computer Science 1770, pp. 651–660. Springer (2000).CrossRefGoogle Scholar
  21. 21.
    Clementi, A., Ianni, M.D., Silvestri, R.: The minimum broadcast range assignment problem on linear multi-hop wireless networks. Theoretical Computer Science 299, 751–761 (2003).CrossRefGoogle Scholar
  22. 22.
    Clementi, A., Penna, P., Silvestri, R.: On the power assignment problem in radio networks. Mobile Networks and Applications 9 125–140 (2004).CrossRefGoogle Scholar
  23. 23.
    Conti, M., Giordano, S.: Multi-hop ad hoc Networking: the reality. IEEE Communications Magazine 45 88–95 (2007).CrossRefGoogle Scholar
  24. 24.
    Conti, M., Crowcroft, J., Passarella, A.: Multi-Hop Ad Hoc Networks from Theory to Reality. Nova Science Publishers (2007).Google Scholar
  25. 25.
    Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C. Introduction to Algorithms, 2nd Edition. MIT Press and McGraw-Hill (2001).Google Scholar
  26. 26.
    Das, G.K., Das, S., Nandy, S.C.: Range assignment for energy efficient broadcasting in linear radio networks. Theoretical Computer Science 352, 332–341 (2006).CrossRefGoogle Scholar
  27. 27.
    Das, G.K., Ghosh, S., Nandy, S.C.: An efficient heuristic algorithm for 2D h-hops range assignment problem. In: Proceedings of IEEE GLOBECOM’04, pp. 1051–1055 (2004).Google Scholar
  28. 28.
    Das, A.K., Marks, R.J., El-Sharkawi, E., Arabshahi, P., Gray, A.: Minimum power broadcast trees for wireless networks: integer programming formulations. In: Proceedings of IEEE INFOCOM’03, pp. 1001–1110 (2003).Google Scholar
  29. 29.
    Das, A.K., Marks, R.J., El-Sharkawi, E., Arabshahi, P., Gray, A.: Optimization methods for minimum power bidirectional topology construction in wireless networks with sectored antennas. In: Proceedings of IEEE GLOBECOM’05, pp. 3962–3968 (2005).Google Scholar
  30. 30.
    Das, A.K., Marks, R.J., El-Sharkawi, E., Arabshahi, P., Gray, A.: r-shrink: a heuristic for improving minimum power broadcast trees in wireless networks. In: Proceedings of IEEE GLOBECOM’03, pp. 523–527 (2003).Google Scholar
  31. 31.
    Fortnow, L.: The Status of the P Versus NP Problem. Communications of the ACM 52(9), 78–86 (2009).CrossRefGoogle Scholar
  32. 32.
    ILOG CPLEX 10.0, Users’ Manual, 2006.Google Scholar
  33. 33.
    Kang, I., Poovendran, R.: Iterated local optimization for minimum energy broadcast. In: Proceedings of the 3rd IEEE International Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks (WiOpt’05), pp. 332–341 (2005).Google Scholar
  34. 34.
    Khoury, B.N., Pardalos, P.M., Hearn, D.W.: Equivalent formulations for the Steiner problem in graphs. In Du, D.Z. et al. (eds.), Network Optimization Problems, pp. 111–123. World Scientific Publishing, Singapore, 1993.Google Scholar
  35. 35.
    Kirousis, L.M., Kranakis, E., Krizanc, D., Pelc, A.: Power consumption in packet radio networks. In: Lecture Note in Computer Science 1200, pp. 363–374 (1997).CrossRefGoogle Scholar
  36. 36.
    Klasing, R., Navarra, A., Papadopoulos, A., P´erennes, S.: Adaptive broadcast consumption (ABC), a new heuristic and new bounds for the minimum energy broadcast routing problem. In: Lecture Notes in Computer Science 2042, pp. 866–877, Springer (2004).Google Scholar
  37. 37.
    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 (MOBIHOC’02), pp. 112–122, 2002.Google Scholar
  38. 38.
    Min, M., Prokopyev, O.A., Pardalos, P.M.: Optimal solutions to minimum total energy broadcasting problem in wireless ad hoc networks. Journal of Combinatorial Optimization 11, 59–69 (2006).CrossRefGoogle Scholar
  39. 39.
    Montemanni, R., Gambardella, L.M.: Exact algorithms for the minimum power symmetric connectivity problem in wireless networks. Computers & Operations Research 32, 2891–2904 (2005).CrossRefGoogle Scholar
  40. 40.
    Montemanni, R., Gambardella, L.M., Das, A.K.: Models and algorithms for the MPSCP: an overview. In Wu, J. (ed.) Handbook on Theoretical and Algorithmic Aspects of Sensor, Ad Hoc Wireless, and Peer-to-Peer Networks, pp. 133–146. Auerbach Publications (2006).Google Scholar
  41. 41.
    Navarra, A.: Tighter bounds for the minimum energy broadcasting problem. In: Proceedings of the 3rd International Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless (WiOpt 2005), pp. 313–322 (2005).Google Scholar
  42. 42.
    Nguyen, G.D.: General algorithms for construction of broadcast and multicast trees with applications to wireless networks. Journal of Communications and Networks 7, 263–277 (2005).Google Scholar
  43. 43.
    Papadimitriou, I., Georgiadis, L.: Minimum-energy broadcasting in multi-hop wireless networks using a single broadcast tree. Mobile Networks and Applications 11, 361–375 (2006).CrossRefGoogle Scholar
  44. 44.
    Perkins, C.E.: Ad Hoc Networking. Addison-Wesley (2001).Google Scholar
  45. 45.
    Polzin, T., Daneshmand, S.V.: A comparison of Steiner tree relaxations. Discrete Applied Mathematics 112, 241–261 (2001).CrossRefGoogle Scholar
  46. 46.
    Ramanathan R., Rosales-Hain, R.: Topology control of multihop wireless networks using transmit power adjustment. In Proceedings of IEEE INFOCOM’00, pp. 404–413 (2000).Google Scholar
  47. 47.
    Wan, P.-J., Călinescu, G., Li, X.-Y., Frieder, O.: Minimum-energy broadcast routing in static ad hoc wireless networks. Wireless Networks 8 607–617 (2002).CrossRefGoogle Scholar
  48. 48.
    Wan, P.-J., Călinescu, G., Yi, C.-W.: Minimum-power multicast routing in static ad hoc wireless networks. IEEE/ACM Transactions on Networking 12, 507–514 (2004).CrossRefGoogle Scholar
  49. 49.
    Wieselthier, J.E., Nguyen, G.D., Ephremides, A.: On the construction of energy-efficient broadcast and multicast trees in wireless networks. In: Proceedings of IEEE INFOCOM’00, pp. 585–594 (2000).Google Scholar
  50. 50.
    Wieselthier, J.E., Nguyen, G.D., Ephremides, A.: Algorithms for energy-efficient multicasting in static ad hoc wireless networks. Mobile Networks and Applications 6, 251–263 (2001).CrossRefGoogle Scholar
  51. 51.
    Wieselthier, J.E., Nguyen, G.D., Ephremides, A.: Distributed algorithms for energy-efficient broadcasting in ad hoc networks. In: Proceedings of IEEE MILCOM’02, pp. 820–825 (2002).Google Scholar
  52. 52.
    Wieselthier, J.E., Nguyen, G.D., Ephremides, A.: Energy-efficient broadcast and multicast trees in wireless networks, Mobile Networks and Applications 7, 481–492 (2002).CrossRefGoogle Scholar
  53. 53.
    Yuan, D.: Computing optimal or near-optimal trees for minimum-energy broadcasting in wireless networks. In: Proceedings of the third international symposium on modeling and optimization in mobile, ad hoc, and wireless networks (WiOpt’05), pp. 323–331 (2005).Google Scholar
  54. 54.
    Yuan, D: An integer programming approach for the minimum-energy broadcast problem in wireless networks. In: Proceedings of the International Network Optimization Conference (INOC), pp. 643-650 (2005).Google Scholar
  55. 55.
    Yuan, D., Bauer, J., Haugland, D.: Minimum-energy broadcast and multicast in wireless networks: an integer programming approach and improved heuristic algorithms. Ad Hoc Networks 6, 696–717 (2008).CrossRefGoogle Scholar

Copyright information

© Springer New York 2011

Authors and Affiliations

  1. 1.Department of InformaticsUniversity of BergenBergenNorway
  2. 2.Department of Science and TechnologyLinköping UniversityNorrköpingSweden

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