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In this paper we prove improved lower and upper bounds for the location of mobile facilities (in Loo and L2 metrics) under the motion of clients when facility moves faster than clients. This paper continues the research started in our joint paper where we present lower bounds and efficient algorithms for exact and approximate maintenance of the 1center for a set of moving points in the plane. Our algorithms are based on the kinetic framework introduced by Basch, Guibas and Hershberger. R.doi:10.1007/978-0-387-35608-2_5 dblp:conf/ifipTCS/BespamyatnikhBKS02 fatcat:4emhq2vpafftjavwrt6duidjau