  In this paper we challenge the widely accepted premise that, in order to
carry out a distributed computation, say on the cloud, users have to inform,
along with all the inputs that the algorithm in use requires, the number of
processors to be used. We discuss the complicated nature of deciding the value
of such parameter, should it be chosen optimally, and propose the alternative
scenario in which this choice is passed on to the server side for automatic
determination. We show that the allocation problem arising from this
alternative is NP-hard only weakly, being therefore solvable in
pseudo-polynomial time. In our proposal, one key component on which the
automatic determination of the number of processors is based is the cost model.
The one we use, which is being increasingly adopted in the wake of the
cloud-computing movement, posits that each single execution of a program is to
be subject to current circumstances on both user and server side, and as such
be priced independently of all others. Running through our proposal is thus a
critique of the established common sense that sizing a set of processors to
handle a submission to some provider is entirely up to the user.
