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...

equivalent ways: in terms of the size of the largest vertex set in a tree decomposition of the graph, in terms of the size of the largest clique in a chordal...

method, the hypertree decomposition, uses a different measure. Either way, the width of a decomposition is defined so that decompositions of size bounded by...

decomposition, decomposition of ideals into primary ideals Tree decomposition, homomorphism of a graph to a tree Vector decomposition, decomposition of vectors...

theory, a branch-decomposition of an undirected graph G is a hierarchical clustering of the edges of G, represented by an unrooted binary tree T with the edges...

property that is held by all cards). decomposition See tree decomposition, path decomposition, or branch-decomposition. degenerate degeneracy A k-degenerate...

path-decomposition is a tree decomposition (X,T) in which the underlying tree T of the decomposition is a path graph. The width of a path-decomposition is...

theory, including the interplay among graph minors, matroid theory, tree decomposition, and infinite graphs. He holds the chair of discrete mathematics at...

triplets pts = reshape(Img, [], 3); % Create OcTree decomposition object using a target bin capacity OT = OcTree(pts, 'BinCapacity', ceil((size(pts, 1) / 256)...

decomposition (also called heavy path decomposition) is a technique for decomposing a rooted tree into a set of paths. In a heavy path decomposition,...

bucket splits. The tree directory follows the spatial decomposition of the quadtree. A tree-pyramid (T-pyramid) is a "complete" tree; every node of the...

algorithm works on the tree decomposition. In general, a constraint satisfaction problem can be solved by first creating a tree decomposition and then using a...

as the decomposition of chordal graphs or strangulated graphs, no edges should be removed. In other contexts, such as the SPQR-tree decomposition of graphs...

In linear algebra, a QR decomposition, also known as a QR factorization or QU factorization, is a decomposition of a matrix A into a product A = QR of...

them. Decomposition relies on chemical processes similar to digestion in animals; in fact, many sources use the words digestion and decomposition interchangeably...

the ear decomposition with the fewest even ears. A tree ear decomposition is a proper ear decomposition in which the first ear is a single edge and for each...

represented by the subtree of the tree decomposition descending from that bag. When G has bounded treewidth, it has a tree decomposition in which all bags have bounded...

easily derive a logarithmic upper bound on the tree-depth. The same technique, applied to a tree decomposition of a graph, shows that, if the treewidth of...

separator hierarchy which may take the form of either a tree decomposition or a branch-decomposition of the graph. Separator hierarchies may be used to devise...

structures underlying the SPQR tree, the triconnected components of a graph, and the connection between this decomposition and the planar embeddings of...

graph. That is, a branch-decomposition may be viewed as a hierarchical clustering of the edges of the graph. Branch-decompositions and an associated numerical...

including directed rooted tree, out-arborescence, out-tree, and even branching being used to denote the same concept. Rooted tree itself has been defined...

of decomposition techniques could be used in order to decrease the size of an equation set: decomposition-recombination planning algorithms, tree decomposition...

decomposition. Decomposition can be a gradual process for organisms that have extended periods of dormancy. One can differentiate abiotic decomposition from biotic...

forms a tree decomposition of the graph, with treewidth equal to one less than the size of the largest clique in the graph; the tree decomposition of any...

a tree decomposition of an undirected graph, one less than the size of the largest vertex-set in the decomposition. Width of a path decomposition of...

A tree stump is the remaining portion of a tree trunk and its roots that remain after a tree has been felled or has naturally fallen. The roots often remain...

In graph theory, the modular decomposition is a decomposition of a graph into subsets of vertices called modules. A module is a generalization of a connected...

tree Fault tree Free tree Game tree K-ary tree Octree Parse tree Phylogenetic tree Polytree Positional tree PQ tree R-tree Rooted tree Ordered tree Recursive...

tree. Decomposition methods generalize join-tree clustering by grouping variables in such a way the resulting problem has a join tree. Decomposition methods...