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In this paper, we study locating charging station problem as facilitylocation problem and its variants ($k$-Median, $k$-Facility location and$k$-center). We study the connectivity and the capacity constraints in theseproblem.  Capacity and connectivity constraints have been studied in the literatureseparately for all these problems. We give first constant factor approximationswhen both the constraints are present. Extending/modifying the techniques usedfor connected variants of the problem to include capacities or for capacitatedvariants of problem to include connectivity is a tedious and challenging task.In this paper, we combine the two constraints by reducing the problem tounderlying well studied problems, solving them as black box and combine theobtained solutions. We also, combine the two constraints in theprize-collection set up.  In the prize-collecting set up, the problems are not even studied when one ofthe constraint is present. We present constant factor approximation for them aswell.

Locating Charging Stations: Connected, Capacitated and Prize- Collecting