The Minimum Manhattan Network Problem: A Fast Factor-3 Approximation

  • Marc Benkert
  • Alexander Wolff
  • Florian Widmann
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3742)


Given a set of nodes in the plane and a constant t ≥ 1, a Euclidean t-spanner is a network in which, for any pair of nodes, the ratio of the network distance and the Euclidean distance of the two nodes is at most t. These networks have applications in transportation or communication network design and have been studied extensively.

In this paper we study 1-spanners under the Manhattan (or L 1-) metric. Such networks are called Manhattan networks. A Manhattan network for a set of nodes can be seen as a set of axis-parallel line segments whose union contains an x- and y-monotone path for each pair of nodes. It is not known whether it is NP-hard to compute minimum Manhattan networks, i.e. Manhattan networks of minimum total length. In this paper we present a factor-3 approximation algorithm for this problem. Given a set of n nodes, our algorithm takes O(n log n) time and linear space.


Line Segment Point Pair Input Point Additional Segment Segment Endpoint 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Marc Benkert
    • 1
  • Alexander Wolff
    • 1
  • Florian Widmann
    • 1
  1. 1.Faculty of Computer ScienceKarlsruhe UniversityKarlsruheGermany

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