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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
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List ranking can equivalently be viewed as performing a prefix sum operation on the given list, in which the values to be summed are all equal to one. The list ranking problem can be used to solve many problems on trees via an Euler tour technique, in which one forms a linked list that includes two copies of each edge of the tree, one in each direction, places the nodes of this list into an ...
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 ...
In computer science, join-based tree algorithms are a class of algorithms for self-balancing binary search trees. This framework aims at designing highly-parallelized algorithms for various balanced binary search trees. The algorithmic framework is based on a single operation join. [1]
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).