Consider a set of mobile computing clients in a certain town who each need to be connected to one of several possible base stations. Suppose there are n clients, with the position of each client specified by its (x, y) coordinate in the plane. There are also k base stations; the position of each of these is also specified by its (x, y) coordinate in the plane. 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: (i) there is a range parameter r, and a client can only be connected to a base station that is within distance r, (ii) there is a load parameter L, and 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 above data, decide whether it is possible to assign every client to a base station subject to the two constraints.
Consider a set of mobile computing clients in a certain town who each need to be
connected to one of several possible base stations. Suppose there are n clients, with
the position of each client specified by its (x, y) coordinate in the plane. There are
also k base stations; the position of each of these is also specified by its (x, y)
coordinate in the plane. 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: (i)
there is a range parameter r, and a client can only be connected to a base station that
is within distance r, (ii) there is a load parameter L, and no more than L clients can
be connected to any single base station. Your goal is to design a polynomial time
possible to assign every client to a base station subject to the two constraints.
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