Skip to main content

Abstract

Wireless ad hoc networks consist of autonomous nodes and require each node’s cooperation in communications. Since the network environment does not assume any infrastructure, communication tasks are performed in an ad-hoc fashion and many well-established protocols for wired networks are not applicable in such a network. In this chapter, we survey several combinatorial optimization. problems in wireless ad hoc networks and discuss applications of the problems. To improve the solution quality, the intrinsic natures of wireless communications should be considered in designing algorithms.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover 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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  • R.K. Ahuja, T.L. Magnanti, and J.B. Orlin. Network Flows: Theory, Algorithms, and Applications. Prentice Hall, Englewood Cliffs, New Jersey, 1993.

    Google Scholar 

  • Y.P. Aneja. An integer linear programming approach to the steiner problem in graphs. Networks, 10:167–178, 1980.

    Article  MATH  MathSciNet  Google Scholar 

  • L. Bahiense, F. Barahona, and O. Porto. Solving steiner tree problems in graphs with lagrangian relaxation. Journal of Combinatorial Optimization, 7:259–282, 2003.

    Article  MATH  MathSciNet  Google Scholar 

  • J.E. Beasley. An algorithm for the steiner problem in graphs. Networks, 14:147–159, 1984.

    Article  MATH  MathSciNet  Google Scholar 

  • R.E. Bellman. On a routing problem. Quarterly of Applied Mathematics, 16:87–90, 1958.

    MATH  MathSciNet  Google Scholar 

  • R. Bixby, 1996. Personal Communication.

    Google Scholar 

  • S. Butenko, X. Cheng, D.-Z. Du, and P.M. Pardalos. On the construction of virtual backbone for ad hoc wireless network. In S. Butenko, R. Murphey, and P.M. Pardalos, editors, Cooperative Control: Models, Applications and Algorithms, pages 43–54. Kluwer Academic Publishers, 2002.

    Google Scholar 

  • S. Butenko, X. Cheng, C.A.S. Oliveira, and P.M. Pardalos. A new heuristic for the minimum connected dominating set problem on ad hoc wireless networks. In S. Butenko, R. Murphey, and P.M. Pardalos, editors, Recent Developments in Cooperative Control and Optimization, pages 61–73. Kluwer Academic Publishers, 2003.

    Google Scholar 

  • M. Cagalj, J.-P. Hubaux, and C. Enz. Minimum-energy broadcast in all-wireless networks: Np-completeness and distribution issues. In Proceedings of the international conference on Mobile computing and networking, pages 172–182, 2002.

    Google Scholar 

  • M. Cardei, X. Cheng, X. Cheng, and D.-Z. Du. Connected domination in multihop ad hoc wireless networks. In Proceedings of the International Conference on Computer Science and Informatics, pages 251–255, 2002.

    Google Scholar 

  • M.X. Cheng, J. Sun, M. Min, and D.-Z. Du. Energy-efficient broadcast and multicast routing in ad hoc wireless networks. In Proceedings of the IEEE International Conference on Performance, Computing, and Communications Conference, pages 87–94, 2003a.

    Google Scholar 

  • X. Cheng, X. Huang, D. Li, and D.-Z. Du. A polynomial-time approximation scheme for the minimum-connected dominating set in ad-hoc wireless networks. Networks, 42:202–208, 2003b.

    Article  MATH  MathSciNet  Google Scholar 

  • S. Chopra and M.R. Rao. The steiner tree problem i: Formulations, compositions and extension of facets. Mathematical Programming: Series A, 64:209–229, 1994a.

    Article  MathSciNet  Google Scholar 

  • S. Chopra and M.R. Rao. The steiner tree problem ii: Properties and classes of facets. Mathematical Programming: Series A, 64:231–246, 1994b.

    Article  MathSciNet  Google Scholar 

  • V. Chvatal. A greedy heuristic for the set-covering problem. Mathematics of Operations Research, 4:233–235, 1979.

    Article  MATH  MathSciNet  Google Scholar 

  • B.N. Clark, C.J. Colboum, and D.S. Johnson. Unit disk graphs. Discrete Mathematics, 86:165–177, 1990.

    Article  MATH  MathSciNet  Google Scholar 

  • A. Claus and N. Maculan. Une nouvelle formulation du problème de steiner sur un graphe. Technical Report 280, Centre de Recerche sur les Transports, Université de Montreal, 1983.

    Google Scholar 

  • B. Das and V. Bharghavan. Routing in ad-hoc networks using minimum connected dominating sets. In Proceedings of the IEEE International Conference on Communications, pages 376–380, 1997.

    Google Scholar 

  • B. Das, R. Sivakumar, and V. Bharghavan. Routing in ad-hoc networks using a spine. In International Conference on Computers and Communications Networks’ 97, Las Vegas, NV, September 1997.

    Google Scholar 

  • S. Deering and D. Cheriton. Multicast routing in datagram internetworks and extended lans. ACM Transactions on Computer Systems, 8:85–111, 1990.

    Article  Google Scholar 

  • E.W. Dijkstra. A note on two problems in connexion with graphs. Numerical Mathematics, 1:262–271, 1959.

    Article  MathSciNet  Google Scholar 

  • M. Doar and I. Leslie. How bad is naive multicast routing. In Proceedings of the Annual Joint Conference of the IEEE Computer and Communications Societies, pages 82–89, 1993.

    Google Scholar 

  • C. Duin and A. Volgenant. Reduction tests for the steiner problem in graphs. Operations Research Letters, 19:549–567, 1989.

    MATH  MathSciNet  Google Scholar 

  • A. Ephremides, J.E. Wieselthier, and D.J. Baker. A design concept of reliable mobile radio networks with frequency hopping signaling. In Proceedings of the IEEE, pages 56–73, 1987.

    Google Scholar 

  • H. Esbensen. Computing near-optimal solutions to the steiner problem in a graph using a genetic algorithm. Networks, 26:173–185, 1995.

    Article  MATH  Google Scholar 

  • M.R. Garey and D.S. Johnson. Computers and Intractibility: A Guide to the Theory of NP-completeness. W. H. Freeman, San Francisco, 1979.

    MATH  Google Scholar 

  • M. Gendreau, J.-F. Larochelle, and B. Sansò. A tabu search heuristic for the steiner tree problem. Networks, 34:162–172, 1998.

    Article  Google Scholar 

  • M. Gerla and J.T.C. Tsai. Multicluster, mobile, multimedia radio network. Wireless Networks, 1:225–265, 1995.

    Article  Google Scholar 

  • M.X. Goemans and Y.S. Myung. A catalog of steiner tree formulations. Networks, 23:19–28, 1993.

    Article  MATH  MathSciNet  Google Scholar 

  • L. Gouveia and T.L. Magnanti. Network flow models for designing diameter-constrained minimum-spanning and steiner trees. Networks, 41:159–173, 2003.

    Article  MATH  MathSciNet  Google Scholar 

  • S. Guha and S. Khuller. Approximation algorithms for connected dominating sets. Algorithmica, 20:374–387, 1998.

    Article  MATH  MathSciNet  Google Scholar 

  • S.L. Hakimi. Steiner’s problem in graphs and its implications. Networks, 1:113–133, 1971.

    Article  MATH  MathSciNet  Google Scholar 

  • F. Hwang and D. Richards. Steiner tree problems. Networks, 22:55–89, 1992.

    Article  MATH  MathSciNet  Google Scholar 

  • F. Hwang, D. Richards, and P. Winter. The Steiner Tree Problem, volume 53 of Annals of Discrete Mathematics. Elsevier, Amsterdam: North-Holland, 1992.

    MATH  Google Scholar 

  • T. Koch and A. Martin. Solving steiner tree problems in graphs to optimality. Networks, 32:207–232, 1998.

    Article  MATH  MathSciNet  Google Scholar 

  • L. Kou, G. Markowsky, and L. Berman. A fast algorithm for steiner trees. Acta Informatica, 15:141–145, 1981.

    Article  MATH  MathSciNet  Google Scholar 

  • B. Liang and Z.J. Haas. Virtual backbone generation and maintenance in ad hoc network mobility management. In Proceedings of the Annual Joint Conference of the IEEE Computer and Communications Societies, pages 1293–1302, 2000.

    Google Scholar 

  • N. Maculan. The steiner problem in graphs. Annals of Discrete Mathematics, 31: 185–212, 1987.

    MathSciNet  Google Scholar 

  • M.V. Marathe, H. Breu, H.B. Hunt III, S.S. Ravi., and D.J. Rosenkrantz. Simple heuristics for unit graphs. Networks, 25:59–68, 1995.

    Article  MATH  MathSciNet  Google Scholar 

  • M. Min, F. Wang, D.-Z. Du, and P.M. Pardalos. A reliable virtual backbone scheme in mobile ad-hoc networks. In Proceedings of the IEEE International Conference on Mobile Ad Hoc and Sensor Systems, pages 60–69, 2004.

    Google Scholar 

  • E.M. Royer and C.-K. Toh. A review of current routing protocols for ad hoc mobile wireless networks. IEEE Personal Communications Magazines, pages 46–55, April 1999.

    Google Scholar 

  • P. Sinha, R. Sivakumar, and V. Bharghavan. Enhancing ad hoc routing with dynamic virtual infrastructure. In Proceedings of the Annual Joint Conference of the IEEE Computer and Communications Societies, pages 1763–1772, 2001.

    Google Scholar 

  • R. Sivakumar, B. Das, and V. Bharghavan. The clade vertebrata: Spines and routing in ad hoc networks. In Proceedings of the IEEE Symposium on Computers and Communications, pages 599–605, 1998.

    Google Scholar 

  • R. Sivakumar, P. Sinha, and V. Bharghavan. Cedar: A core-extraction distributed ad hoc routing algorithm. IEEE Journal on Selected Areas in Communications, 17: 1454–1465, 1999.

    Article  Google Scholar 

  • I. Stojmenovic, M. Seddigh, and J. Zunic. Dominating sets and neighbor elimination-based broadcasting algorithms in wireless networks. IEEE Transactions of Parallel and Distributed Systems, 12:14–25, 2001.

    Google Scholar 

  • Q. Sun and H. Langendoerfer. Efficient multicast routing for delay-sensitive applications. In Proceedings of the Second Workshop on Protocols for Multimedia Systems(PROMS’ 95), pages 452–458, 1995.

    Google Scholar 

  • H. Takahashi and A. Matsuyama. An approximate solution for the steiner problem for graphs. Mathematica Japonica, 24:573–577, 1980.

    MATH  MathSciNet  Google Scholar 

  • Y.-C. Tseng, S.-Y. Ni, Y.-S. Chen, and J.-P. Sheu. The broadcast storm problem in a mobile ad hoc network. Wireless Networks, 8:153–167, 2002.

    Article  MATH  Google Scholar 

  • S. Voss. Steiner’s problem in graphs: Heuristic methods. Discrete Applied Mathematics, 40:45–72, 1992.

    Article  MATH  MathSciNet  Google Scholar 

  • S. Voss and K. Gutenschwager. A chunking based genetic algorithm for the steiner tree problem in graphs. In P.M. Pardalos and D.-Z. Du, editors, Network Design: Connectivity and Facilities Location, volume 40 of DIMACS Series on Discrete Mathematics and Theoretical Computer Science, pages 335–355. American Mathematical Society, 1998.

    Google Scholar 

  • D. Wall. Mechanisms for Broadcast and Selective Broadcast. PhD thesis, Stanford University, 1980.

    Google Scholar 

  • P.-J. Wan, K. M. Alzoubi, and O. Frieder. Distributed construction of connected dominating set in wireless ad hoc networks. Mobile Networks and Applications, 9: 141–149, 2004a.

    Article  Google Scholar 

  • P.-J. Wan, G. Calinescu, X.-Y. Li, and O. Frieder. Minimum-energy broadcasting in static ad hoc wireless networks. Wireless Networks, 8:607–617, 2002.

    Article  MATH  Google Scholar 

  • P.-J. Wan, G. Calinescu, and C.-W. Yi. Minimum-power multicast routing in static ad hoc wireless networks. IEEE/ACM Transactions on Networking, 12:507–514, 2004b.

    Article  Google Scholar 

  • J.E. Wieselthier, G.D. Nguyen, and A. Ephremides. Energy-efficient broadcast and multicast trees in wireless networks. Mobile Networks and Applications, 7:481–492, 2002.

    Article  Google Scholar 

  • P. Winter. Steiner problems in networks: Survey. Networks, 17:129–167, 1987.

    Article  MATH  MathSciNet  Google Scholar 

  • R.T. Wong. A dual ascent approach for steiner tree problems on a directed graph. Mathematical Programming, 28:271–287, 1984.

    Article  MATH  MathSciNet  Google Scholar 

  • J. Wu and H. Li. On calculating connected dominating set for efficient routing in ad hoc wireless networks. In Proceedings of the international workshop on Discrete algorithms and methods for mobile computing and communications, pages 7–14, 1999.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer Science+Business Media, Inc.

About this chapter

Cite this chapter

Min, M., Chinchuluun, A. (2006). Optimization in Wireless Networks. In: Resende, M.G.C., Pardalos, P.M. (eds) Handbook of Optimization in Telecommunications. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-30165-5_31

Download citation

Publish with us

Policies and ethics