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.

给定一个几何空间和一组加权空间点，大小受限的k个简单多边形（SCkSP）问题可识别k个简单的多边形，这些多边形可最大化多边形所覆盖的空间点的总权重并满足多边形大小的约束。SCkSP问题对于许多社会应用程序都很重要，包括热点区域检测和资源分配。这个问题很难解决。由于存在大量的空间点和多边形大小限制，因此在计算上具有挑战性。我们的初步工作为SCkSP引入了最近邻三角剖分和合并（NNTM）算法，以在最大空间点总权重的同时满足大小约束。但是，我们发现NNTM算法的性能取决于t-最近图。在本文中，我们扩展了先前的工作，并提出了一种优于先前工作的新颖方法。使用芝加哥犯罪和美国联邦野火数据集的实验表明，该算法大大降低了我们先前工作的计算成本，并提供了更好的解决方案。