A 1.5-Approximation of the Minimal Manhattan Network Problem

  • Sebastian Seibert
  • Walter Unger
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3827)


Given a set of points in the plane, the Minimal Manhattan Network Problem asks for an axis-parallel network that connects every pair of points by a shortest path under L 1-norm (Manhattan metric). The goal is to minimize the overall length of the network.

We present an approximation algorithm that provides a solution of length at most 1.5 times the optimum. Previously, the best known algorithm has given only a 2-approximation.


Short Path Line Segment Grid Line Admissible Solution Vertical Line Segment 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Althöfer, I., Das, G., Dobkin, D., Joseph, D., Soares, J.: On Sparse Spanners of Weighted Graphs. Discrete Comput. Geoam. 9, 81–100 (1993)zbMATHCrossRefGoogle Scholar
  2. 2.
    Benkert, M., Shirabe, T., Wolff, A.: The Minimum Manhattan Network Problem—Approximations and Exact Solution. In: Proc. 20th European Workshop on Computational Geometry (EWCG 2004), pp. 209–212 (2004)Google Scholar
  3. 3.
    Benkert, M., Wolff, A., Widmann, F.: The Minimum Manhattan Network Problem: A Fast Factor-3 Approximation. In: Akiyama, J., Kano, M., Tan, X. (eds.) JCDCG 2004. LNCS, vol. 3742, pp. 85–86. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  4. 4.
    Chandra, B., Das, G., Narasimhan, G., Soares, J.: New Sparseness Resuls on Graph Spanners. Internat. J. Comput. Geom. Appl. 5, 125–144 (1995)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Chen, D., Das, G., Smid, M.: Lower bounds for computing geometric spanners and approximate shortest paths. Discrete Applied Math. 110, 151–167 (2001)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Chepoi, V., Nouioua, K., Vaxes, Y.: A rounding algorithm for approximating minimum Manhattan networks. In: Chekuri, C., Jansen, K., Rolim, J.D.P., Trevisan, L. (eds.) APPROX 2005 and RANDOM 2005. LNCS, vol. 3624, pp. 40–51. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  7. 7.
    Das, G., Narasimhan, G.: A Fast Algorithm for Constructing Sparse Euclidian Spanners. Internat. J. Comput. Geom. Appl. 7, 297–315 (1997)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Gudmundsson, J., Levcopoulos, C., Narasimhan, G.: Approximating a Minimum Manhattan Network. Nordic J. Computing 8, 219–232 (2001)zbMATHMathSciNetGoogle Scholar
  9. 9.
    Gudmundsson, J., Levcopoulos, C., Narasimhan, G.: Fast Greedy Algorithms for Constructing Sparse Geometric Spanners. SIAM J. Computing 31, 1479–1500 (2002)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Kato, R., Imai, K., Asano, T.: An Improved Algorithm for the Minimum Manhattan Network Problem. In: Bose, P., Morin, P. (eds.) ISAAC 2002. LNCS, vol. 2518, pp. 344–356. Springer, Heidelberg (2002)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Sebastian Seibert
    • 1
  • Walter Unger
    • 2
  1. 1.Department Informatik, ETH ZentrumETH ZürichZürich
  2. 2.Lehrstuhl für Informatik IRWTH AachenAachen

Personalised recommendations