On the Tightness of a Cut-Set Bound on Network Function Computation

The following model of network function computation in directed acyclic networks is considered: A sink node desires to compute correctly a target function with all possible inputs of the function generated at multiple source nodes. The network links have limited capacity and are error-free. The intermediate network nodes perform network coding without any computation bound. The computing rate is measured by the average number of times that the target function can be computed for one use of the network. Guang, Yang and Li recently proposed a general upper bound on the computing capacity that is tight for all the instances of the problem with known computing capacity in literature. In this paper, we show that their upper bound is not tight in general by explicitly characterizing the computing capacity of an example. Our technique can be extended to characterize upper bounds on the computing capacity of a general instance of the network function computing problem.