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We consider the optimal transmission of distributed correlated discretememoryless sources across a network with capacity constraints. We presentseveral previously undiscussed structural properties of the set of feasiblerates and transmission schemes. We extend previous results concerning theintersection of polymatroids and contrapolymatroids to characterize when all ofthe vertices of the Slepian-Wolf rate region are feasible for the capacityconstrained network. An explicit relationship between the conditionalindependence relationships of the distributed sources and the number ofvertices for the Slepian-Wolf rate region are given. These properties are thenapplied to characterize the optimal transmission rate and scheme and itsconnection to the corner points of the Slepian-Wolf rate region. In particular,we demonstrate that when the per-source compression costs are in tension withthe per-link flow costs the optimal flow/rate point need not coincide with avertex of the Slepian-Wolf rate region. Finally, we connect results for thesingle-sink problem to the multi-sink problem by extending structural insightsand developing upper and lower bounds on the optimal cost of the multi-sinkproblem.

Structural and Optimization Properties for Joint Selection of Source Rates and Network Flow