Near-optimal clustering in the k-machine model

The clustering problem, in its many variants, has numerous applications operations research and computer science (e.g., bioinformatics, image processing, social network analysis, etc.). As sizes of data sets have grown rapidly, researchers focused on designing algorithms for problems models computation suited large-scale such as MapReduce, Pregel, streaming models. k-machine model (Klauck et al., (SODA 2015) [8]) is a simple, message-passing distributed graph processing. This paper considers three the most prominent examples problems: uncapacitated facility location p-median p-center problem presents O(1)-factor approximation these running O˜(n/k) rounds model. These are optimal up to polylogarithmic factors because this also shows Ω˜(n/k) lower bounds obtaining polynomial-factor problems. first results We assume that metric provided input only implicitly provided, an edge-weighted nutshell, our main technical contribution show constant-factor all can be obtained by learning small portion metric.