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Size constrained k simple polygons

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Abstract

Given a geometric space and a set of weighted spatial points, the Size Constrained k Simple Polygons (SCkSP) problem identifies k simple polygons that maximize the total weights of the spatial points covered by the polygons and meet the polygon size constraint. The SCkSP problem is important for many societal applications including hotspot area detection and resource allocation. The problem is NP-hard; it is computationally challenging because of the large number of spatial points and the polygon size constraint. Our preliminary work introduced the Nearest Neighbor Triangulation and Merging (NNTM) algorithm for SCkSP to meet the size constraint while maximizing the total weights of the spatial points. However, we find that the performance of the NNTM algorithm is dependent on the t-nearest graph. In this paper, we extend our previous work and propose a novel approach that outperforms our prior work. Experiments using Chicago crime and U.S. Federal wildfire datasets demonstrate that the proposed algorithm significantly reduces the computational cost of our prior work and produces a better solution.

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Acknowledgements

We would like to thank the National Science Foundation CAREER under Grant No. 1844565.

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Authors and Affiliations

  1. Computer Science, Florida Atlantic University, 777 Glades Road, Boca Raton, FL, 33431-0991, USA

    KwangSoo Yang & Valmer Huhn

  2. School of Computer, Information, and Communications Engineering, Kunsan National University, 558 Daehak-ro, Gunsan, 55140, South Korea

    Kwang Woo Nam

  3. Computer Engineering, Florida Atlantic University, Boca Raton, FL, 33431, USA

    Ahmad Qutbuddin

  4. Computer Science, Georgia Institute of Technology, Atlanta, GA, 30332, USA

    Aaron Reich

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  1. KwangSoo Yang
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Correspondence to KwangSoo Yang.

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Yang, K., Nam, K.W., Qutbuddin, A. et al. Size constrained k simple polygons. Geoinformatica 25, 43–67 (2021). https://doi.org/10.1007/s10707-020-00416-9

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