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{\bssdoz CME 305: Discrete Mathematics and Algorithms}
{\\ \bssten Instructor: Professor John Tomlin (jtomlin5@stanford.edu) }
{\\ \bssten HW\#2 --  Due Thursday 01/28/13}
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The Transshipment problem is a minimum cost network flow problem with no capacities on the arcs. It may have several sources and several terminals (sinks). A Transportation problem (Hitchcock---Koopmans problem) is a minimum cost flow problem on a bipartite network, where all the left hand nodes are sources and all the right hand nodes are terminals. Assume that the sum of the resources at the source nodes equals the sum of the demands at the terminals, and there are no capacities on the arcs.
\begin{enumerate}
\item 
Prove that every such Transshipment problem is equivalent to a Transportation problem.
\item 
Prove that every basis (i.e. set of linearly independent columns) of a Transshipment problem corrresponds to a tree subgraph of the network.
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