  Let a cluster (network) of sensors be connected by the communication links,
each link having a capacity upper bound. Each sensor observes a discrete random
variable in private and one sensor serves as a cluster header or sink. Here, we
formulate the problem of how to let the sensors encode their observations such
that the direction of compressed data is a feasible flow towards the sink. We
demonstrate that this problem can be solved by an existing maximum independent
flow (MIF) algorithm in polynomial time. Further, we reveal that this algorithm
in fact determines an optimal solution by recursively pushing the remaining
randomness in the sources via unsaturated communication links towards the sink.
We then show that the MIF algorithm can be implemented in a distributed manner.
For those networks with integral communication capacities, we propose an
integral MIF algorithm which completes much faster than MIF. Finally, we point
out that the nature of the data compression problem in a sensor cluster is to
seek the maximum independent information flow in the intersection of two
submodular polyhedra, which can be further utilized to improve the MIF
algorithm in the future.
