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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]
In graph theory, a tree decomposition is a mapping of a graph into a tree that can be used to define the treewidth of the graph and speed up solving certain computational problems on the graph. Tree decompositions are also called junction trees , clique trees , or join trees .
Graph algorithms solve problems related to graph theory. Subcategories. This category has the following 3 subcategories, out of 3 total. ... Junction tree algorithm ...
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 ...
Given the tree of a decomposition, solving can be done by constructing the binary tree-like problem as described above, and solving it. This is a polynomial-time problem, as it can be solved in polynomial time using, for example, an algorithm for enforcing directional arc consistency.
A clique tree or junction tree is a tree of cliques, used in the junction tree algorithm. A chain graph is a graph which may have both directed and undirected edges, but without any directed cycles (i.e. if we start at any vertex and move along the graph respecting the directions of any arrows, we cannot return to the vertex we started from if ...
NP-complete special cases include the edge dominating set problem, i.e., the dominating set problem in line graphs. NP-complete variants include the connected dominating set problem and the maximum leaf spanning tree problem. [3]: ND2 Feedback vertex set [2] [3]: GT7 Feedback arc set [2] [3]: GT8 Graph coloring [2] [3]: GT4
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).