Facility Location in Evolving Metrics

Understanding the dynamics of evolving social or infrastructure networks is a challenge in applied areas such as epidemiology, viral marketing, or urban planning. During the past decade, data has been collected on such networks but has yet to be fully analyzed. We propose to use information on the d...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2014-03
Main Authors: Eisenstat, David, Mathieu, Claire, Schabanel, Nicolas
Format: Article
Language:English
Subjects:
Algorithms
Approximation
Epidemiology
Evolution
Leasing
Marketing
Operations research
Site selection
Switching theory
Time dependence
Urban planning
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Understanding the dynamics of evolving social or infrastructure networks is a challenge in applied areas such as epidemiology, viral marketing, or urban planning. During the past decade, data has been collected on such networks but has yet to be fully analyzed. We propose to use information on the dynamics of the data to find stable partitions of the network into groups. For that purpose, we introduce a time-dependent, dynamic version of the facility location problem, that includes a switching cost when a client's assignment changes from one facility to another. This might provide a better representation of an evolving network, emphasizing the abrupt change of relationships between subjects rather than the continuous evolution of the underlying network. We show that in realistic examples this model yields indeed better fitting solutions than optimizing every snapshot independently. We present an \(O(\log nT)\)-approximation algorithm and a matching hardness result, where \(n\) is the number of clients and \(T\) the number of time steps. We also give an other algorithms with approximation ratio \(O(\log nT)\) for the variant where one pays at each time step (leasing) for each open facility.
ISSN:2331-8422