A Polynomial-Time Approximation Scheme for Facility Location on Planar Graphs

Abstract : We consider the classic FACILITY LOCATION problem on planar graphs (non-uniform, uncapacitated). Given an edge-weighted planar graph G, a set of clients C ⊆ V (G), a set of facilities F ⊆ V (G), and opening costs open : F → R 0 , the goal is to find a subset D of F that minimizes c∈C min f ∈D dist(c, f) + f ∈D open(f). The FACILITY LOCATION problem remains one of the most classic and fundamental optimization problem for which it is not known whether it admits a polynomial-time approximation scheme (PTAS) on planar graphs despite significant effort for obtaining one. We solve this open problem by giving an algorithm that for any ε > 0, computes a solution of cost at most (1 + ε) times the optimum in time n 2 O(ε −2 log(1/ε)) .
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Contributor : Vincent Cohen-Addad <>
Submitted on : Wednesday, November 13, 2019 - 9:12:39 AM
Last modification on : Friday, November 22, 2019 - 1:34:03 AM
Long-term archiving on: Friday, February 14, 2020 - 2:08:20 PM


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  • HAL Id : hal-02360765, version 1
  • ARXIV : 1904.10680


Vincent Cohen-Addad, Marcin Pilipczuk, Michał Pilipczuk. A Polynomial-Time Approximation Scheme for Facility Location on Planar Graphs. FOCS'19, Nov 2019, Baltimore, United States. ⟨hal-02360765⟩



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