Geometric Spanner of Objects under L1 Distance

  • Yongding Zhu
  • Jinhui Xu
  • Yang Yang
  • Naoki Katoh
  • Shin-ichi Tanigawa
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5092)


Geometric spanner is a fundamental structure in computational geometry and plays an important role in many geometric networks design applications. In this paper, we consider the following generalized geometric spanner problem under L 1 distance: Given a set of disjoint objects S, find a spanning network G with minimum size so that for any pair of points in different objects of S, there exists a path in G with length no more than t times their L 1 distance, where t is the stretch factor. Specifically, we focus on three types of objects: rectilinear segments, axis aligned rectangles, and rectilinear monotone polygons. By combining ideas of t-weekly dominating set, walls, aligned pairs and interval cover, we develop a 4-approximation algorithm (measured by the number of Steiner points) for each type of objects. Our algorithms run in near quadratic time, and can be easily implemented for practical applications.


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© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Yongding Zhu
    • 1
  • Jinhui Xu
    • 1
  • Yang Yang
    • 1
  • Naoki Katoh
    • 2
  • Shin-ichi Tanigawa
    • 2
  1. 1.Department of Computer Science and EngineeringState University of New York at BuffaloBuffaloUSA
  2. 2.Department of Architecture and Architectural SystemsKyoto UniversityJapan

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