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International Symposium on Algorithms and Computation

ISAAC 2012: Algorithms and Computation pp 332–341Cite as

Optimal Point Movement for Covering Circular Regions

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7676))

Abstract

Given n points in a circular region C in the plane, we study the problem of moving these points to the boundary of C to form a regular n-gon such that the maximum of the Euclidean distances traveled by the points is minimized. These problems find applications in mobile sensor barrier coverage of wireless sensor networks. The problem further has two versions: the decision version and optimization version. In this paper, we present an O(nlog2 n) time algorithm for the decision version and an O(nlog3 n) time algorithm for the optimization version. The previously best algorithms for these two problem versions take O(n 3.5) time and O(n 3.5logn) time, respectively. A by-product of our techniques is an algorithm for dynamically maintaining the maximum matching of a circular convex bipartite graph; our algorithm performs each vertex insertion or deletion on the graph in O(log2 n) time. This result may be interesting in its own right.

Chen’s research was supported in part by NSF under Grant CCF-0916606. Work by Tan was partially supported by Grant-in-Aid (MEXT/JPSP KAKENHI 23500024) for Scientific Research from Japan Society for the Promotion of Science.

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Author information

Authors and Affiliations

  1. Department of Computer Science and Engineering, University of Notre Dame, Notre Dame, IN, 46556, USA

    Danny Z. Chen

  2. Tokai University, 4-1-1 Kitakaname, Hiratsuka, 259-1292, Japan

    Xuehou Tan

  3. Department of Computer Science, Utah State University, Logan, UT, 84322, USA

    Haitao Wang

  4. State Key Lab. for Novel Software Technology, Nanjing University, Hankou Road 22, Nanjing, 210093, China

    Gangshan Wu

Authors
  1. Danny Z. Chen
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  2. Xuehou Tan
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  3. Haitao Wang
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  4. Gangshan Wu
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Editor information

Editors and Affiliations

  1. Department of Computer Science and Information Engineering, National Taiwan University, 1 Roosevelt Road, Section 4, 106, Taipei, Taiwan

    Kun-Mao Chao

  2. Institute of Information Science, Academia Sinica, 128 Academia Road, Section 2, 115, Taipei, Taiwan

    Tsan-sheng Hsu

  3. Department of Computer Science and Engineering, National Chung Hsing University, 250 Kuo Kuang Road, 402, Taichung, Taiwan

    Der-Tsai Lee

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© 2012 Springer-Verlag Berlin Heidelberg

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Chen, D.Z., Tan, X., Wang, H., Wu, G. (2012). Optimal Point Movement for Covering Circular Regions. In: Chao, KM., Hsu, Ts., Lee, DT. (eds) Algorithms and Computation. ISAAC 2012. Lecture Notes in Computer Science, vol 7676. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35261-4_36

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  • DOI: https://doi.org/10.1007/978-3-642-35261-4_36

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-35260-7

  • Online ISBN: 978-3-642-35261-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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