(1+ Є)-approximation for facility location in data streams

@ space. Our PTAS is significantly faster than any previously known (1 + e)-approximation algorithm for the problem, and is also relatively simple. Our algorithm for dynamic geometric data streams is the first (1 + e)-approximation algorithm for the cost of the facility location problem with polylogarithmic space, and it resolves an open problem in the streaming area. Both algorithms are based on a novel and simple decomposition of an input point set P into small subsets Pi, such that: • the cost of solving the facility location problem for each Pi is small (which means that for each Pi one needs to open only a small, polylogarithmic number of facilities), •

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