Shao, Jiating; Xu, Dachuan; Wang, Fengmin Approximation algorithms for the squared metric \(k\)-level facility location problem. (Chinese. English summary) Zbl 1374.90275 Acta Math. Appl. Sin. 39, No. 4, 586-597 (2016). Summary: In this paper, we study the squared metric \(k\)-level facility location problem where the facilities are on \(k\)-level. The objective is to minimize the sum of the opening cost and the connection cost. Using the LP-rounding techniques, we then propose an approximation algorithm and obtain the approximation ratio of \(9\). Furthermore, we study the squared metric \(k\)-level soft capacitied facility location problem. Using the LP-rounding techniques, we then propose an approximation algorithm and obtain the approximation ratio of \(12.2216\). MSC: 90B80 Discrete location and assignment 90C59 Approximation methods and heuristics in mathematical programming 90C05 Linear programming Keywords:squared metric; \(k\)-level facility location; soft capacity; approximation algorithm PDFBibTeX XMLCite \textit{J. Shao} et al., Acta Math. Appl. Sin. 39, No. 4, 586--597 (2016; Zbl 1374.90275)