Dynamic facility location via exponential clocks

Hyung Chan An, Ashkan Norouzi-Fard, Ola Svensson

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 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 connect 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
Title of host publicationProceedings of the 26th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2015
PublisherAssociation for Computing Machinery
Pages708-721
Number of pages14
EditionJanuary
ISBN (Electronic)9781611973747
DOIs
Publication statusPublished - 2015 Jan 1
Event26th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2015 - San Diego, United States
Duration: 2015 Jan 42015 Jan 6

Publication series

NameProceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms
NumberJanuary
Volume2015-January

Other

Other26th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2015
CountryUnited States
CitySan Diego
Period15/1/415/1/6

All Science Journal Classification (ASJC) codes

  • Software
  • Mathematics(all)

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    An, H. C., Norouzi-Fard, A., & Svensson, O. (2015). Dynamic facility location via exponential clocks. In Proceedings of the 26th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2015 (January ed., pp. 708-721). (Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms; Vol. 2015-January, No. January). Association for Computing Machinery. https://doi.org/10.1137/1.9781611973730.48