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In a tree, every edge breaks the graph in two parts. The constraint passed along an edge tells how the part of the originating end of the edge affects the variables of the destination node. In other words, a constraint passed from node <math>i</math> to node <math>j</math> tells how the nodes "on the side of <math>i</math>" constrain the variables of node <math>j</math>.
If the variables of these two nodes are <math>X_i</math> and <math>X_j</math>, the nodes on the
The algorithm proceeds from the leaves of the tree. In each node, the summaries of its children (if any) are collected. These summary and the constraint of the node are used to generate the summary of the node for its parent. When the root is reached, the process is inverted: the summary of each node for each child is generated and sent it. When all leaves are reached, the algorithm stops.
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| year=2001
| url=http://www.springerlink.com/(rqc54x55rqwetq55eco03ymp)/app/home/contribution.asp?referrer=parent&backto=issue,5,61;journal,1765,3346;linkingpublicationresults,1:105633,1
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| first=Georg
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