Consider a set of mobile computing clients in a certain town who each need to be connected to one of several possible base stations. We'll suppose there are n clients, with the position of each client specified by its (x, y) coordinates in the plane. There are also k base stations; the position of each of these is specified by (x, y) coordinates as well.
For each client, we wish to connect it to exactly one of the base stations. Our choice of connections is constrained in the following ways.
There is a range parameter r–a client can only be connected to a base station that is within distance r. There is also a load parameter L–no more than L clients can be connected to any single base station.
Your goal is to design a polynomial-time algorithm for the following problem. Given the positions of a set of clients and a set of base stations, as well as the range and load parameters, decide whether every client can be connected simultaneously to a base station, subject to the range and load conditions in the previous paragraph.
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