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Algorithmica

, Volume 57, Issue 3, pp 562–584 | Cite as

Kinetic Facility Location

  • Bastian Degener
  • Joachim Gehweiler
  • Christiane Lammersen
Article

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. In our scenario, 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 in total, where \(R:=\frac{\max_{p_{i}\in\mathcal{P}}{f_{i}}\cdot\max_{p_{i}\in\mathcal{P}}{d_{i}}}{\min_{p_{i}\in\mathcal {P}}{f_{i}}\cdot\min_{p_{i}\in\mathcal{P}}{d_{i}}}\) , ℘={p 1,p 2,…,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.

Keywords

Facility location Kinetic data structure Approximation algorithm Deterministic algorithm 

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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  • Bastian Degener
    • 1
    • 2
  • Joachim Gehweiler
    • 2
  • Christiane Lammersen
    • 3
  1. 1.International Graduate School Dynamic Intelligent SystemsPaderborn UniversityPaderbornGermany
  2. 2.Heinz Nixdorf Institute, Computer Science DepartmentPaderborn UniversityPaderbornGermany
  3. 3.Computer Science Department IUniversity of BonnBonnGermany

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