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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 ...
Tree decomposition (Junction tree) and treewidth; Graph triangulation (see also Chordal graph) Perfect order; Hidden Markov model. Baum–Welch algorithm; Viterbi algorithm; Incidence matrix; Independent set problem; Knowledge representation. Conceptual graph; Mind map; Level structure; Link popularity; Mac Lane's planarity criterion; Node ...
1 Relation to junction trees. 4 comments. 2 The recursion for Independent Set. 1 comment. 3 Books? 1 comment. 4 Treewidth of trees. 2 comments. 5 junction tree. 3 ...
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 ...
Minimum k-spanning tree; Minor testing (checking whether an input graph contains an input graph as a minor); the same holds with topological minors; Steiner tree, or Minimum spanning tree for a subset of the vertices of a graph. [2] (The minimum spanning tree for an entire graph is solvable in polynomial time.)
In computer science, parallel tree contraction is a broadly applicable technique for the parallel solution of a large number of tree problems, and is used as an algorithm design technique for the design of a large number of parallel graph algorithms. Parallel tree contraction was introduced by Gary L. Miller and John H. Reif, [1] and has ...