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Generalized Voronoi diagrams for a ladder: II. Efficient construction of the diagram

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Abstract

We present a collection of algorithms, all running in timeO(n 2 logn α (n)o(α(n)3)) for some fixed integers(where α(n) is the inverse Ackermann's function), for constructing a skeleton representation of a suitably generalized “Voronoi diagram” for a ladder moving in a two-dimensional space bounded by polygonal barriers consisting ofn line segments. This diagram, which is a two-dimensional subcomplex of the dimensional configuration space of the ladder, is introduced and analyzed in a companion paper by the present authors. The construction of the diagram described in this paper yields a motion-planning algorithm for the ladder which runs within the same time bound given above.

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Authors and Affiliations

  1. Computer Science Department, Courant Institute of Mathematical Sciences, 251 Mercer Street, 10012, New York, NY, USA

    Colm Ó'Dúnlaing, Micha Sharir & Chee Yap

  2. School of Mathematical Sciences, Tel Aviv University, Tel Aviv, Israel

    Micha Sharir

Authors
  1. Colm Ó'Dúnlaing
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  2. Micha Sharir
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  3. Chee Yap
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Additional information

Communicated by Bernard Chazelle.

Work on this paper has been supported in part by Office of Naval Research Grant N00014-82-K-0381, and by grants from the Digital Equipment Corporation, the Sloan Foundation, the System Development Foundation, the IBM corporation, and by National Science Foundation CER Grant No. DCR-8320085. Work by the second author has also been supported in part by a grant from the US-Israeli Binational Science Foundation.

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Ó'Dúnlaing, C., Sharir, M. & Yap, C. Generalized Voronoi diagrams for a ladder: II. Efficient construction of the diagram. Algorithmica 2, 27–59 (1987). https://doi.org/10.1007/BF01840348

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  • DOI: https://doi.org/10.1007/BF01840348

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