Dynamic facility location via exponential clocks

Hyung-Chan An, Ashkan Norouzi-Fard, Ola Svensson

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

The dynamic facility location problem is a generalization of the classic facility location problem proposed by Eisenstat, Mathieu, and Schabanel to model the dynamics of evolving social/infrastructure networks. The generalization lies in that the distance metric between clients and facilities changes over time. This leads to a trade-off between optimizing the classic objective function and the "stability" of the solution: There is a switching cost charged every time a client changes the facility to which it is connected. While the standard linear program (LP) relaxation for the classic problem naturally extends to this problem, traditional LP-rounding techniques do not, as they are often sensitive to small changes in the metric resulting in frequent switches. We present a new LP-rounding algorithm for facility location problems, which yields the first constant approximation algorithm for the dynamic facility location problem. Our algorithm installs competing exponential clocks on the clients and facilities and connects every client by the path that repeatedly follows the smallest clock in the neighborhood. The use of exponential clocks gives rise to several properties that distinguish our approach from previous LP roundings for facility location problems. In particular, we use no clustering and we allow clients to connect through paths of arbitrary lengths. In fact, the clustering-free nature of our algorithm is crucial for applying our LP-rounding approach to the dynamic problem.

Original languageEnglish
Article number21
JournalACM Transactions on Algorithms
Volume13
Issue number2
DOIs
Publication statusPublished - 2017 Feb 1

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Facility Location
Facility Location Problem
Linear Program
Rounding
Clustering
Path
Distance Metric
Dynamic Problem
Approximation Algorithms
Switch
Infrastructure
Objective function
Trade-offs
Metric
Costs
Arbitrary

All Science Journal Classification (ASJC) codes

  • Mathematics (miscellaneous)

Cite this

An, Hyung-Chan ; Norouzi-Fard, Ashkan ; Svensson, Ola. / Dynamic facility location via exponential clocks. In: ACM Transactions on Algorithms. 2017 ; Vol. 13, No. 2.
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Dynamic facility location via exponential clocks. / An, Hyung-Chan; Norouzi-Fard, Ashkan; Svensson, Ola.

In: ACM Transactions on Algorithms, Vol. 13, No. 2, 21, 01.02.2017.

Research output: Contribution to journalArticle

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