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International Computing and Combinatorics Conference

COCOON 2001: Computing and Combinatorics pp 121–130Cite as

On the Planar Two-Watchtower Problem

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2108))

Abstract

In this paper we study the following planar two-watchtower problem: given a terrain (X-monotone chain) T with n vertices, locate two vertical segments (watchtowers) /uv and /u′v′ which have to be erected on T such that every point on T is visible to the top of either watchtowers (u or u′) and the maximum height of /uv, /u′v′ is minimized. We present an O(n 4) time algorithm to solve the discrete version of this problem when v, v′ must be on some vertices of T. Under a mild condition on solving a special cubic equation with three bounded variables in O(f 3) time we can also generalize the algorithm to solve the general problem in O(n 4 +n 3 f 3) time. Using parametric search, the discrete problem can be solvedin O(n 3 log2 n) time and the general problem can be solved in O(n 4 log2 n) time.

This research is supportedb y Research Grants Council of Hong Kong SAR, China (CERG Project No. CityU1103/99E) anda MONTS grant.

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of British Columbia, Vancouver, B.C., V6T 1Z4, Canada

    Sergei Bespamyatnikh

  2. Department of Computer Science, University of Texas at Pan American, Edinburg, TX, 78539-2999, USA

    Zhixiang Chen

  3. School of Management, Xi’an Jiaotong University, Shaanxi, China

    Kanliang Wang

  4. Department of Computer Science, Montana State University, Bozeman, MT, 59717-3880, USA

    Binhai Zhu

Authors
  1. Sergei Bespamyatnikh
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  2. Zhixiang Chen
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  3. Kanliang Wang
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  4. Binhai Zhu
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Massachusetts, One University Avenue, Lowell, MA, 01854, USA

    Jie Wang

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© 2001 Springer-Verlag Berlin Heidelberg

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Bespamyatnikh, S., Chen, Z., Wang, K., Zhu, B. (2001). On the Planar Two-Watchtower Problem. In: Wang, J. (eds) Computing and Combinatorics. COCOON 2001. Lecture Notes in Computer Science, vol 2108. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44679-6_14

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  • DOI: https://doi.org/10.1007/3-540-44679-6_14

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42494-9

  • Online ISBN: 978-3-540-44679-8

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