Online Facility Location with Weights and Congestion

Authors Arghya Chakraborty , Rahul Vaze

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Arghya Chakraborty
  • Tata Institute of Fundamental Research, Mumbai, India
Rahul Vaze
  • Tata Institute of Fundamental Research, Mumbai, India


The first author wishes to extend his deepest thanks to Prof. Umang Bhaskar, Prof. Prahladh Harsha, and Prof. Jaikumar Radhakrishnan for the thought-provoking discussions and the valuable advice they generously shared with him on multiple occasions.

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Arghya Chakraborty and Rahul Vaze. Online Facility Location with Weights and Congestion. In 43rd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 284, pp. 6:1-6:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


The classic online facility location problem deals with finding the optimal set of facilities in an online fashion when demand requests arrive one at a time and facilities need to be opened to service these requests. In this work, we study two variants of the online facility location problem; (1) weighted requests and (2) congestion. Both of these variants are motivated by their applications to real life scenarios and the previously known results on online facility location cannot be directly adapted to analyse them. - Weighted requests: In this variant, each demand request is a pair (x,w) where x is the standard location of the demand while w is the corresponding weight of the request. The cost of servicing request (x,w) at facility F is w⋅ d(x,F). For this variant, given n requests, we present an online algorithm attaining a competitive ratio of 𝒪(log n) in the secretarial model for the weighted requests and show that it is optimal. -Congestion: The congestion variant considers the case when there is a congestion cost that grows with the number of requests served by each facility. For this variant, when the congestion cost is a monomial, we show that there exists an algorithm attaining a constant competitive ratio. This constant is a function of the exponent of the monomial and the facility opening cost but independent of the number of requests.

Subject Classification

ACM Subject Classification
  • Theory of computation → Online algorithms
  • online algorithms
  • online facility location
  • probabilistic method
  • weighted-requests
  • congestion


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