Approximating Minimum Manhattan Networks in Higher Dimensions

  • Aparna Das
  • Emden R. Gansner
  • Michael Kaufmann
  • Stephen Kobourov
  • Joachim Spoerhase
  • Alexander Wolff
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6942)


We consider the minimum Manhattan network problem, which is defined as follows. Given a set of points called terminals in ℝ d , find a minimum-length network such that each pair of terminals is connected by a set of axis-parallel line segments whose total length is equal to the pair’s Manhattan (that is, L 1-) distance. The problem is NP-hard in 2D and there is no PTAS for 3D (unless \({\cal P}\!=\!{\cal NP}\)). Approximation algorithms are known for 2D, but not for 3D.

We present, for any fixed dimension d and any \(\ensuremath{\varepsilon} >0\), an \(O(n^\ensuremath{\varepsilon} )\)-approximation. For 3D, we also give a 4(k − 1)-approximation for the case that the terminals are contained in the union of k ≥ 2 parallel planes.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Aparna Das
    • 1
  • Emden R. Gansner
    • 2
  • Michael Kaufmann
    • 3
  • Stephen Kobourov
    • 1
  • Joachim Spoerhase
    • 4
  • Alexander Wolff
    • 4
  1. 1.Dept. of Comp. Sci.University of ArizonaTucsonU.S.A.
  2. 2.AT&T Labs ResearchFlorham ParkU.S.A.
  3. 3.Wilhelm-Schickard-Institut für InformatikUniversität TübingenGermany
  4. 4.Institut für InformatikUniversität WürzburgGermany

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