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A Fast 2-Approximation Algorithm for the Minimum Manhattan Network Problem

  • Zeyu Guo
  • He Sun
  • Hong Zhu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5034)

Abstract

Given a set T of n points in ℝ2, a Manhattan Network G is a network with all its edges horizontal or vertical segments, such that for all p,q ∈ T, in G there exists a path (named a Manhattan path) of the length exactly the Manhattan distance between p and q. The Minimum Manhattan Network (MMN) problem is to find a Manhattan network of the minimum length, i.e., the total length of the segments of the network is to be minimized. In this paper we present a 2-approximation algorithm with time complexity O(n 2), which improves the 2-approximation algorithm with time complexity Ω(n 8), proposed by Chepoi, Nouioua et al.. To the best of our knowledge, this is the best result on this problem.

Keywords

Vertical Strip Vertical Segment Horizontal Segment Horizontal Strip Convex Corner 
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.
    Benkert, M., Wolff, A., Widmann, F.: The minimum Manhattan network problem: a fast factor-3 approximation. Technical Report 2004-16, Fakultät für Informatik, Universität Karlsruhe. In: Proceedings of the 8th Japanese Conference on Discrete and Computational Geometry, pp. 16–28 (2005) (A sort version appeared)Google Scholar
  2. 2.
    Benkert, M., Shirabe, T., Wolff, A.: The minimum Manhattan network problem: approximations and exact solution. In: Proceedings of the 20th European Workshop on Computational Geometry, pp. 209–212 (2004)Google Scholar
  3. 3.
    Chalmet, G., Francis, L., Kolen, A.: Finding efficient solutions for rectilinear distance location problems efficiently. European Journal of Operations Research 6, 117–124 (1981)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Chepoi, V., Nouioua, K., Vaxès, Y.: A rounding algorithm for approximating minimum Manhattan networks. Theoretical Computer Science 390, 56–69 (2008) Preliminary version appeared. In: Proceedings of the 8th International Workshop on Approximation Algorithms for Combinatorial Optimization, pp. 40–51 (2005)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Frances Yao, F.: Efficient dynamic programming using quadrangle inequalities. In: Proceedings of the 12th Annual ACM Symposium on Theory of Computing, pp. 429–435 (1980)Google Scholar
  6. 6.
    Gudmundsson, J., Levcopoulos, C., Narasimhan, G.: Approximating a minimum Manhattan network. Nordic Journal of Computing 8, 219–232 (2001); Preliminary version appeared. In: Proceedings of the 2nd International Workshop on Approximation Algorithms for Combinatorial Optimization, pp. 28–37 (1999)zbMATHMathSciNetGoogle Scholar
  7. 7.
    Kato, R., Imai, K., Asano, T.: An improved algorithm for the minimum Manhattan network problem. In: Proceedings of the 13th International Symposium on Algorithms and Computation, pp. 344–356 (2002)Google Scholar
  8. 8.
    Lam, F., Alexandersson, M., Pachter, L.: Picking alignments from (Steiner) trees. Journal of Computational Biology 10, 509–520 (2003)CrossRefGoogle Scholar
  9. 9.
    Seibert, S., Unger, W.: A 1.5-approximation of the minimal Manhattan network problem. In: Proceedings of the 16th International Symposium on Algorithms and Computation, pp. 246–255 (2005)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Zeyu Guo
    • 1
  • He Sun
    • 2
  • Hong Zhu
    • 3
  1. 1.Department of Computer Science and EngineeringFudan UniversityChina
  2. 2.Shanghai Key Laboratory of Intelligent Information ProcessingFudan UniversityChina
  3. 3.Shanghai Key Laboratory of Trustworthy ComputingEast China Normal UniversityChina

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