The recent large scale availability of mobility data, which captures individual mobility patterns, poses novel operational problems that are exciting and challenging. Motivated by this, we introduce and study a variant of the (cost-minimization) facility location problem where each individual is endowed with two locations (hereafter, her home and work locations), and the connection cost is the minimum distance between any of her locations and its closest facility. We design a polynomial-time algorithm whose approximation ratio is at most 2.497. We complement this positive result by showing that the proposed algorithm is at least a 2.428-approximation, and there exists no polynomial-time algorithm with approximation ratio $2-\epsilon$ under UG-hardness. We further extend our results and analysis to the model where each individual is endowed with K locations. Finally, we conduct numerical experiments over both synthetic data and US census data (for NYC, greater LA, greater DC, Research Triangle) and evaluate the performance of our algorithms.

翻译：近期，大规模移动数据的可用性（这些数据捕捉了个体移动模式）带来了既令人兴奋又充满挑战的新型运营问题。受此启发，我们引入并研究了一种（成本最小化）设施选址问题的变体，其中每个个体拥有两个位置（以下称为其家庭和工作地点），连接成本是任意一个位置到其最近设施的最小距离。我们设计了一种多项式时间算法，其近似比至多为2.497。我们通过证明该算法至少是一个2.428近似算法，并且基于UG难题假设，不存在近似比为$2-\epsilon$的多项式时间算法，来补充这一正面结果。我们进一步将结果和分析扩展到每个个体拥有K个位置的模型。最后，我们在合成数据和美国人口普查数据（针对纽约市、大洛杉矶地区、大华盛顿特区和研究三角区）上进行了数值实验，并评估了我们算法的性能。