Advertisement

Annals of Operations Research

, Volume 238, Issue 1–2, pp 41–68 | Cite as

Geometric partitioning and robust ad-hoc network design

  • John Gunnar CarlssonEmail author
  • Mehdi Behroozi
  • Xiang Li
Article
  • 179 Downloads

Abstract

We present fast approximation algorithms for the problem of dividing a given convex geographic region into smaller sub-regions so as to distribute the workloads of a set of vehicles. Our objective is to partition the region in such a fashion as to ensure that vehicles are capable of communicating with one another under limited communication radii. We consider variations of this problem in which sub-regions are constrained to have equal area or be convex, and as a side consequence, our approach yields a factor 1.99 approximation algorithm for the continuous k-centers problem on a convex polygon.

Keywords

Geometric partitioning Network design Location set covering Vehicle routing approximation algorithms 

Supplementary material

10479_2015_2093_MOESM1_ESM.pdf (197 kb)
Supplementary material 1 (pdf 197 KB)

References

  1. Alzoubi, K. M., Wan, P.-J., & Frieder, O. (2002) Message-optimal connected dominating sets in mobile ad hoc networks. In Proceedings of the 3rd ACM international symposium on mobile ad hoc networking and computing, (pp 157–164).Google Scholar
  2. Aronov, B., Carmi, P., & Katz, M. J. (2009). Minimum-cost load-balancing partitions. Algorithmica, 54(3), 318–336.CrossRefGoogle Scholar
  3. Avis, D., & Toussaint, G. T. (1981). An efficient algorithm for decomposing a polygon into star-shaped polygons. Pattern Recognition, 13(6), 395–398.CrossRefGoogle Scholar
  4. Bereg, S., Bose, P., & Kirkpatrick, D. (2006). Equitable subdivisions within polygonal regions. Computational Geometry, 34(1), 20–27.CrossRefGoogle Scholar
  5. Berman, O., Drezner, Z., Tamir, A., & Wesolowsky, G. O. (2009). Optimal location with equitable loads. Annals of Operations Research, 167(1), 307–325.CrossRefGoogle Scholar
  6. Brimberg, J., & Salhi, S. (2005). A continuous location-allocation problem with zone-dependent fixed cost. Annals of Operations Research, 136(1), 99–115.CrossRefGoogle Scholar
  7. Carlsson, J. G. (2012). Dividing a territory among several vehicles. INFORMS Journal on Computing, 24(4), 565–577.CrossRefGoogle Scholar
  8. Carlsson, J. G., Ge, D., Subramaniam, A., & Ye. Y. (2007). Solving the min–max multi-depot vehicle routing problem. In Proceedings of the FIELDS workshop on global optimization.Google Scholar
  9. Haugland, D., Ho, S. C., & Laporte, G. (2007). Designing delivery districts for the vehicle routing problem with stochastic demands. European Journal of Operational Research, 180(3), 997–1010.CrossRefGoogle Scholar
  10. Hochbaum, D. S. (1997). Approximation algorithms for NP-hard problems, volume 20. PWS publishing company Boston.Google Scholar
  11. Melissen, J. B. M., & Schuur, P. C. (2000). Covering a rectangle with six and seven circles. Discrete Applied Mathematics, 99(1), 149–156.CrossRefGoogle Scholar
  12. Pavone, M., Arsie, A., Frazzoli, E., & Bullo, F. (2011). Distributed algorithms for environment partitioning in mobile robotic networks. Automatic Control, IEEE Transactions on, 56(8), 1834–1848.CrossRefGoogle Scholar
  13. Preparata, F. P., & Shamos, M. I. (1985). Computational geometry: An introduction. New York: Springer.CrossRefGoogle Scholar
  14. Royer, E. M., Melliar-Smith, P. M., & Moser, L. E. (2001). An analysis of the optimum node density for ad hoc mobile networks. In IEEE International Conference on Communications, 2001. ICC 2001 (Vol. 3, pp. 857–861).Google Scholar
  15. Stojmenovic, I. (2002). Position-based routing in ad hoc networks. IEEE Communications Magazine, 40(7), 128–134.CrossRefGoogle Scholar
  16. Valiente, G. (2013). Algorithms on trees and graphs. Berlin: Springer.Google Scholar
  17. Wattenhofer, R., Li, L., Bahl, P., & Wang, Y.-M. (2001) Distributed topology control for power efficient operation in multihop wireless ad hoc networks. In INFOCOM 2001. Twentieth annual joint conference of the IEEE computer and communications societies. Proceedings. IEEE (Vol. 3, pp. 1388–1397)Google Scholar
  18. Wu J., & Li, H. (1999) On calculating connected dominating set for efficient routing in ad hoc wireless networks. In Proceedings of the 3rd international workshop on Discrete algorithms and methods for mobile computing and communications, (pp. 7–14).Google Scholar
  19. Youla, D. C., & Webb, H. (1982). Image restoration by the method of convex projections: Part 1: Theory. IEEE Transactions on Medical Imaging, 1(2), 81–94.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • John Gunnar Carlsson
    • 1
    Email author
  • Mehdi Behroozi
    • 1
    • 2
  • Xiang Li
    • 2
  1. 1.Department of Industrial and Systems EngineeringUniversity of Southern CaliforniaLos AngelesUSA
  2. 2.Department of Industrial and Systems EngineeringUniversity of MinnesotaMinneapolisUSA

Personalised recommendations