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Then any maximum-weight spanning tree of the clique graph is a junction tree. So, to construct a junction tree we just have to extract a maximum weight spanning tree out of the clique graph. This can be efficiently done by, for example, modifying Kruskal's algorithm. The last step is to apply belief propagation to the obtained junction tree. [10]
It is a key step of the junction tree algorithm, used in belief propagation on graphical models. A directed acyclic graph The corresponding moral graph, with newly added arcs shown in red
The tree decomposition of a graph is far from unique; for example, a trivial tree decomposition contains all vertices of the graph in its single root node. A tree decomposition in which the underlying tree is a path graph is called a path decomposition, and the width parameter derived from these special types of tree decompositions is known as ...
5 junction tree. 3 comments. 6 Wording of lead. 2 comments. 7 Nice tree decompositions. 1 comment. Toggle the table of contents. Talk: Tree decomposition. Add languages.
Chow and Liu provide a simple algorithm for constructing the optimal tree; at each stage of the procedure the algorithm simply adds the maximum mutual information pair to the tree. See the original paper, Chow & Liu (1968), for full details. A more efficient tree construction algorithm for the common case of sparse data was outlined in Meilă ...
Manual memory management (as in C++) and reference counting have a similar issue of arbitrarily long pauses in case of deallocating a large data structure and all its children, though these only occur at fixed times, not depending on garbage collection. Manual heap allocation. search for best/first-fit block of sufficient size; free list ...
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The algorithm may be modified to start with any particular vertex s by setting C[s] to be a number smaller than the other values of C (for instance, zero), and it may be modified to only find a single spanning tree rather than an entire spanning forest (matching more closely the informal description) by stopping whenever it encounters another ...