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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]
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 ...
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
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.
Parallel all-pairs shortest path algorithm; Parallel breadth-first search; Parallel single-source shortest path algorithm; Path-based strong component algorithm; Pre-topological order; Prim's algorithm; Proof-number search; Push–relabel maximum flow algorithm
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The program evaluation and review technique (PERT) is a statistical tool used in project management, which was designed to analyze and represent the tasks involved in completing a given project. PERT was originally developed by Charles E. Clark for the United States Navy in 1958; it is commonly used in conjunction with the Critical Path Method ...
A bottleneck edge is the highest weighted edge in a spanning tree. A spanning tree is a minimum bottleneck spanning tree if the graph does not contain a spanning tree with a smaller bottleneck edge weight. [1] For a directed graph, a similar problem is known as Minimum Bottleneck Spanning Arborescence (MBSA).