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The Kinetic Facility Location Problem

  • Bastian Degener
  • Joachim Gehweiler
  • Christiane Lammersen
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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Copyright information

© 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

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