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A PTAS for a disc covering problem using width-bounded separators

Author

Listed:
  • Zhixiang Chen

    (University of Texas—Pan American)

  • Bin Fu

    (University of New Orleans
    Research Institute for Children)

  • Yong Tang

    (Sun Yat-Sen University)

  • Binhai Zhu

    (Montana State University)

Abstract

In this paper, we study the following disc covering problem: Given a set of discs of various radii on the plane and centers on the grid points, find a subset of discs to maximize the area covered by exactly one disc. This problem originates from the application in digital halftoning, with the best known approximation factor being 5.83 (Asano et al., 2004). We show that if their radii are between two positive constants, then there exists a polynomial time approximation scheme. Our techniques are based on the width-bounded geometric separator recently developed in Fu and Wang (2004), Fu (2006).

Suggested Citation

  • Zhixiang Chen & Bin Fu & Yong Tang & Binhai Zhu, 2006. "A PTAS for a disc covering problem using width-bounded separators," Journal of Combinatorial Optimization, Springer, vol. 11(2), pages 203-217, March.
    • Handle: RePEc:spr:jcomop:v:11:y:2006:i:2:d:10.1007_s10878-006-7132-y
    DOI: 10.1007/s10878-006-7132-y
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    Citations

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    Cited by:

    1. Tim Wylie & Michael A. Schuh & Rafal A. Angryk, 2016. "Enabling high-dimensional range queries using kNN indexing techniques: approaches and empirical results," Journal of Combinatorial Optimization, Springer, vol. 32(4), pages 1107-1132, November.
    2. Bin Fu & Zhixiang Chen, 2008. "Sublinear time width-bounded separators and their application to the protein side-chain packing problem," Journal of Combinatorial Optimization, Springer, vol. 15(4), pages 387-407, May.

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