  A key aspect of many resource allocation problems is the need for the
resource controller to compute a function, such as the max or arg max, of the
competing users metrics. Information must be exchanged between the competing
users and the resource controller in order for this function to be computed. In
many practical resource controllers the competing users' metrics are
communicated to the resource controller, which then computes the desired
extremization function. However, in this paper it is shown that information
rate savings can be obtained by recognizing that controller only needs to
determine the result of this extremization function. If the extremization
function is to be computed losslessly, the rate savings are shown in most cases
to be at most 2 bits independent of the number of competing users. Motivated by
the small savings in the lossless case, simple achievable schemes for both the
lossy and interactive variants of this problem are considered. It is shown that
both of these approaches have the potential to realize large rate savings,
especially in the case where the number of competing users is large. For the
lossy variant, it is shown that the proposed simple achievable schemes are in
fact close to the fundamental limit given by the rate distortion function.
