Covering Clients with Types and Budgets

Authors Dimitris Fotakis, Laurent Gourvès, Claire Mathieu, Abhinav Srivastav

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Author Details

Dimitris Fotakis
  • Yahoo Research-New York, USA & National Technical University of Athens, Greece
Laurent Gourvès
  • Université Paris-Dauphine, PSL University, CNRS, LAMSADE, 75016 Paris, France
Claire Mathieu
  • CNRS, France
Abhinav Srivastav
  • ENS Paris & Université Paris-Dauphine, France

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Dimitris Fotakis, Laurent Gourvès, Claire Mathieu, and Abhinav Srivastav. Covering Clients with Types and Budgets. In 29th International Symposium on Algorithms and Computation (ISAAC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 123, pp. 73:1-73:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


In this paper, we consider a variant of the facility location problem. Imagine the scenario where facilities are categorized into multiple types such as schools, hospitals, post offices, etc. and the cost of connecting a client to a facility is realized by the distance between them. Each client has a total budget on the distance she/he is willing to travel. The goal is to open the minimum number of facilities such that the aggregate distance of each client to multiple types is within her/his budget. This problem closely resembles to the set cover and r-domination problems. Here, we study this problem in different settings. Specifically, we present some positive and negative results in the general setting, where no assumption is made on the distance values. Then we show that better results can be achieved when clients and facilities lie in a metric space.

Subject Classification

ACM Subject Classification
  • Theory of computation → Packing and covering problems
  • Theory of computation → Facility location and clustering
  • Facility Location
  • Geometric Set Cover
  • Local Search


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