Proximity problems on moving points
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Kinetic data structures: a state of the art report
WAFR '98 Proceedings of the third workshop on the algorithmic foundations of robotics on Robotics : the algorithmic perspective: the algorithmic perspective
Data structures for mobile data
Journal of Algorithms
Mobile facility location (extended abstract)
DIALM '00 Proceedings of the 4th international workshop on Discrete algorithms and methods for mobile computing and communications
A new greedy approach for facility location problems
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
SIAM Journal on Computing
Smooth kinetic maintenance of clusters
Proceedings of the nineteenth annual symposium on Computational geometry
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Deformable spanners and applications
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Algorithms for dynamic geometric problems over data streams
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Approximating extent measures of points
Journal of the ACM (JACM)
A distributed O(1)-approximation algorithm for the uniform facility location problem
Proceedings of the eighteenth annual ACM symposium on Parallelism in algorithms and architectures
A Nearly Linear-Time Approximation Scheme for the Euclidean $k$-Median Problem
SIAM Journal on Computing
Facility location in sublinear time
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
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We present a deterministic kinetic data structure for the facility location problem that maintains a subset of the moving points as facilities such that, at any point of time, the accumulated cost for the whole point set is at most a constant factor larger than the optimal cost. Each point can change its status between client and facility and moves continuously along a known trajectory in a d-dimensional Euclidean space, where dis a constant.Our kinetic data structure requires $\mathcal{O}(n (\log^{d}(n)+\log(nR)))$ space, where $R:=\frac{\max_{p_i \in \mathcal{P}}{f_i} \,\cdot\, \max_{p_i\in \mathcal{P}}{d_i}}{\min_{p_i \in \mathcal{P}}{f_i} \,\cdot\, \min_{p_i\in \mathcal{P}}{d_i}}$, $\mathcal{P} = \{ p_1, p_2, \ldots , p_n \}$ is the set of given points, and fi, diare the maintenance cost and the demand of a point pi, respectively. In case that each trajectory can be described by a bounded degree polynomial, we process $\mathcal{O}(n^2 \log^2(nR))$ events, each requiring $\mathcal{O}(\log^{d+1}(n) \cdot \log(nR))$ time and $\mathcal{O}(\log(nR))$ status changes. To the best of our knowledge, this is the first kinetic data structure for the facility location problem.