An efficient algorithm for the single facility location problem with polyhedral norms and disk-shaped demand regions
研究了需求区域为等半径圆盘、距离由矩形范数（如L1或L∞）度量的单设施选址问题，提出了一个时间复杂度为O(n log^c n)的精确组合算法，其中c仅依赖于空间维度，且算法可推广到其他多面体范数。
The single facility location problem with demand regions seeks for a facility location minimizing the sum of the distances from n demand regions to the facility. The demand regions represent sales markets where the transportation costs are negligible. In this paper, we assume that all demand regions are disks of the same radius, and the distances are measured by a rectilinear norm, e.g. $$\ell _1$$ or $$\ell _\infty $$ . We develop an exact combinatorial algorithm running in time $$O(n\log ^c n)$$ for some c dependent only on the space dimension. The algorithm is generalizable to the other polyhedral norms.