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Applications of a numbering scheme for polygonal obstacles in the plane

  • Session 1: Invited Presentation
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Algorithms and Computation (ISAAC 1996)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1178))

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Abstract

We present efficient algorithms for the problems of matching red and blue disjoint geometric obstacles in the plane and connecting the matched obstacle pairs with mutually nonintersecting paths that have useful geometric properties. We first consider matching n red and n blue disjoint isothetic rectangles and connecting the n matched rectangle pairs with nonintersecting monotone rectilinear paths; each such path consists of O(n) segments and is not allowed to touch any rectangle other than the matched pair that it is linking. Based on a numbering scheme for certain geometric objects and on several useful geometric observations, we develop an O(n log n) time, O(n) space algorithm that produces a desired matching for isothetic rectangles. If an explicit printing of all the n paths is required, then our algorithm takes O(n log n+λ) time and O(n) space, where λ is the total size of the desired output. We then extend these matching algorithms to other classes of red/blue polygonal obstacles. The numbering scheme also finds applications to other problems.

This work was carried out in part at the Center for Applied Science and Engineering and Institute of Information Science. Academia Sinica, Nankang, Taiwan, during its 1996 Summer Institute on Computational Geometry and Applications.

This author gratefully acknowledges support from the National Science Foundation under Grant DCR-9202807, and the COAST Project at Purdue University and its sponsors, in particular Hewlett Packard.

The research of this author was supported in part by the National Science Foundation under Grant CCR-9623585.

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Author information

Authors and Affiliations

  1. Department of Computer Sciences, Purdue University, 47907, West Lafayette, Indiana, USA

    Mikhail J. Atallah

  2. Department of Computer Science and Engineering, University of Notre Dame, 46556, Notre Dame, Indiana, USA

    Danny Z. Chen

Authors
  1. Mikhail J. Atallah
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  2. Danny Z. Chen
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Editor information

Tetsuo Asano Yoshihide Igarashi Hiroshi Nagamochi Satoru Miyano Subhash Suri

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© 1996 Springer-Verlag Berlin Heidelberg

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Atallah, M.J., Chen, D.Z. (1996). Applications of a numbering scheme for polygonal obstacles in the plane. In: Asano, T., Igarashi, Y., Nagamochi, H., Miyano, S., Suri, S. (eds) Algorithms and Computation. ISAAC 1996. Lecture Notes in Computer Science, vol 1178. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0009476

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  • DOI: https://doi.org/10.1007/BFb0009476

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  • Print ISBN: 978-3-540-62048-8

  • Online ISBN: 978-3-540-49633-5

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