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On Some Optimization Problems in Obnoxious Facility Location

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Computing and Combinatorics (COCOON 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1858))

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Abstract

In this paper we study the following general MaxMinoptimization problem concerning undesirable (obnoxious) facility location: Given a set of n sites S inside a convex region P, construct m garbage deposit sites V m such that the minimum distance between these sites V m and the union of S and V m , V m ∪S, is maximized. We present a general method using Voronoi diagrams to approximately solve two such problems when the sites S’s are points and weighted convex polygons (correspondingly, V m’s are points and weighted points and the distances are L 2 and weighted respectively). In the latter case we generalize the Voronoi diagrams for disjoint weighted convex polygons in the plane. Our algorithms run in polynomial time and approximate the optimal solutions of the above two problems by a factor of 2.

The authors would like to acknowledge the support of research grants from NSF of China, Research Grants Council of Hong Kong SAR, China (CERG Project No. CityU1103/99E) and City University of Hong Kong

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Author information

Authors and Affiliations

  1. Dept. of Mathematics, Huazhong University of Science and Technology, China

    Zhongping Qin

  2. School of Management, Xi’an Jiaotong University, Xi’an, China

    Yinfeng Xu

  3. Dept. of Computer Science, City University of Hong Kong, Kowloon, Hong Kong

    Binhai Zhu

Authors
  1. Zhongping Qin
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  2. Yinfeng Xu
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  3. Binhai Zhu
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Editor information

Editors and Affiliations

  1. Department of Computer Science and Engineering, University of Minnesota, MN 55455, Minneapolis, USA

    Ding-Zhu Du

  2. Department of Computer Science and Software Engineering, University of Newcastle, Callaghan, NSW 2308, Australia

    Peter Eades  & Vladimir Estivill-Castro  & 

  3. School of Computer Science and Engineering, University of Newcastle, NSW 2052, Sydney, Australia

    Xuemin Lin  & Arun Sharma  & 

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© 2000 Springer-Verlag Berlin Heidelberg

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Qin, Z., Xu, Y., Zhu, B. (2000). On Some Optimization Problems in Obnoxious Facility Location. In: Du, DZ., Eades, P., Estivill-Castro, V., Lin, X., Sharma, A. (eds) Computing and Combinatorics. COCOON 2000. Lecture Notes in Computer Science, vol 1858. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44968-X_32

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  • DOI: https://doi.org/10.1007/3-540-44968-X_32

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67787-1

  • Online ISBN: 978-3-540-44968-3

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