SWAT 2008: Algorithm Theory – SWAT 2008 pp 378-389

The Kinetic Facility Location Problem

• Bastian Degener
• Joachim Gehweiler
• Christiane Lammersen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5124)

Abstract

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 d is 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 f i , d i are the maintenance cost and the demand of a point p i , 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.

Keywords

facility location kinetic data structure approximation

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© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

• Bastian Degener
• 1
• 2
• Joachim Gehweiler
• 2
• Christiane Lammersen
• 2
1. 1.International Graduate School Dynamic Intelligent Systems
2. 2.Heinz Nixdorf Institute, Computer Science DepartmentPaderborn UniversityPaderbornGermany