Optimization Letters

, Volume 2, Issue 1, pp 99–111 | Cite as

Optimal placement of stereo sensors

  • Mohammad Al Hasan
  • Krishna K. Ramachandran
  • John E. Mitchell
Original Paper


Autonomous wireless devices such as sensor nodes and stereo cameras, due to their low cost of operation coupled with the potential for remote deployment, have found a plethora of applications ranging from monitoring air, soil and water to seismic detection and military surveillance. Typically, such a network spans a region of interest with the individual nodes cooperating to detect events and disseminate information. Given a deployment of sensors and targets over a region, a sensor pairing is desired for each target that optimizes the coverage under certain constraints. This problem can be modeled as an integer programming problem and solved using branch-and-cut. For larger problems, it is necessary to limit the number of variables, and a GRASP routine was developed for this purpose. Valid cutting planes are developed and computational results presented.


Sensors Integer programming Branch-and-cut GRASP 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Aiex R.M., Pardalos P.M., Resende M.G.C. and Toraldo G. (2005). GRASP with path-relinking for three-index assignment. INFORMS J. Comput. 17(2): 224–247 CrossRefMathSciNetGoogle Scholar
  2. 2.
    Akyildiz I.F., Su W., Sankarasubramaniam Y. and Cayirci E. (2002). A survey on sensor networks. IEEE Commun. Mag. 40(8): 102–114 CrossRefGoogle Scholar
  3. 3.
    Bredin, J.L., Demaine, E.D., Hajiaghayi, M.T., Rus, D.: Deploying sensor networks with guaranteed capacity and fault tolerance. In: Proceedings of the 6th ACM International Symposium on Mobile ad hoc Networking and Computing MobiHoc ’05, pp. 309–319 (2005)Google Scholar
  4. 4.
    Chvátal V. (1973). Edmonds polytopes and a hierarchy of combinatorial problems. Discrete Math. 4: 305–337 zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Edmonds J. (1965). Maximum matching and a polyhedron with 0, 1 vertices. J. Res Nat Bureau Stand. 69: 125–130 zbMATHMathSciNetGoogle Scholar
  6. 6.
    Feo T.A. and Resende M.G.C. (1995). Greedy randomized adaptive search procedures. J. Global Optim. 6: 109–133 zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Grundel D., Oliveira C.A.S. and Pardalos P.M. (2004). Asymptotic properties of random multidimensional assignment problems. J. Optim. Theory Appl. 122(3): 487–500 zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Isler V., Khanna S., Spletzer J. and Taylor C.J. (2005). Target tracking with distributed sensors: the focus of attention problem. Comput. Vis Image Understand. J. 100(1-2): 225–247 CrossRefGoogle Scholar
  9. 9.
    Johnsson M., Magyar G. and Nevalainen O. (1998). On the Euclidean 3-matching problem. Nordic J. Comput. 5(2): 143–171 zbMATHMathSciNetGoogle Scholar
  10. 10.
    Li, Y., Pardalos, P.M., Resende, M.G.C.: A greedy randomized adaptive search procedure for the quadratic assignment problem. In: Pardalos, P. M., Wolkowicz, H. (eds.) Quadratic assignment and related problems, vol. 16 ofDIMACS Series in Discrete Mathematics and Theoretical Computer Science, pp. 237–261. American Mathematical Society (1994)Google Scholar
  11. 11.
    Lloyd, E.L., Liu, R., Marathe, M.V., Ramanathan, R., Ravi, S.S.: Algorithmic aspects of topology control problems for ad hoc networks. In: Proceedings of the 3rd ACM International Symposium on Mobile ad hoc Networking and Computing, pp. 123–134 (2002)Google Scholar
  12. 12.
    Pitsoulis L.S. and Resende M.G.C. (2002). Greedy randomized adaptive search procedures. In: Pardalos, P.M. and Resende, M.G.C. (eds) Handbook of Applied Optimization, pp 168–183. Oxford University Press, Oxford Google Scholar
  13. 13.
    Rentala P., Musunuri R., Gandham S., Saxena U. (2003) Survey of sensor networks. Technical Report UTDCS-10-03, Department of Computer Science. University of Texas at Dallas, RichardsonGoogle Scholar
  14. 14.
    Resende M.G.C. and Ribeiro C.C. (2002). Greedy radomized adaptive search procedures. In: Glover, F. and Kochenberger, G. (eds) Handbook of Metaheuristics, pp 219–249. Kluwer, Dordrecht Google Scholar
  15. 15.
    Resende M.G.C and Ribeiro C.C. (2005). GRASP with path relinking: recent advances and applications. In: Ibaraki, T., Nonobe, K. and Yagiura, M. (eds) Metaheuristics: Progress as Real Problem Solvers, pp 301–331. Springer, Berlin Google Scholar
  16. 16.
    Tilak S., Abu-Ghazaleh N. and Heinzelman W. (2002). A taxonomy of wireless micro-sensor network models. ACM Mobile Comput. Commun. Rev. (MC2R) 6(2): 28–36 CrossRefGoogle Scholar
  17. 17.
    Tubaishat M. and Madria S. (2003). Sensor networks: an overview. IEEE Potent. 22(2): 20–23 CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  • Mohammad Al Hasan
    • 1
  • Krishna K. Ramachandran
    • 2
  • John E. Mitchell
    • 3
  1. 1.Department of Computer ScienceRensselaer Polytechnic Institute TroyTroyUSA
  2. 2.Department of ElectricalRensselaer Polytechnic Institute TroyTroyUSA
  3. 3.Department of Mathematical SciencesRensselaer Polytechnic Institute TroyTroyUSA

Personalised recommendations