Facility Location in Evolving Metrics

David Eisenstat (1) , Claire Mathieu (2) , Nicolas Schabanel (3)

1 Brown University - Department of Computer Science
2 ENS-PSL - École normale supérieure - Paris
3 LIAFA - Laboratoire d'informatique Algorithmique : Fondements et Applications

Understanding the dynamics of evolving social or infrastructure networks is a challenge in applied areas such as epidemiology, viral marketing, and urban planning. During the past decade, data has been collected on such networks but has yet to be analyzed fully. 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, which 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 for some realistic examples that this model yields better hypotheses than its counterpart without switching costs, where each snapshot can be optimized independently. For our model, we present an $O(\log nT)$-approximation algorithm and a matching hardness result, where $n$ is the number of clients and $T$ is the number of timesteps. We also give another algorithm with approximation ratio $O(\log nT)$ for a variant model where the decision to open a facility is made independently at each timestep.

Domaines: Algorithme et structure de données [cs.DS]; Réseaux sociaux et d'information [cs.SI]

David Eisenstat, Claire Mathieu, Nicolas Schabanel. Facility Location in Evolving Metrics. ALGOTEL 2014 -- 16èmes Rencontres Francophones sur les Aspects Algorithmiques des Télécommunications, Jun 2014, Le Bois-Plage-en-Ré, France. pp.1-4. ⟨hal-00984375⟩