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...

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

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...

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

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...

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

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, 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...

science which studies decomposition is generally referred to as taphonomy from the Greek word taphos, meaning tomb. Decomposition can also be a gradual...

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...

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...

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...

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...

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...

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

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...

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

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

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...

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

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

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...

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...

different use of 'tangle' appears in Graph minors X. Obstructions to tree-decomposition by N. Robertson and P. D. Seymour, Journal of Combinatorial Theory...

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...

architecture of software systems. It is based on a structural decomposition (a hierarchical tree structure) of a system into containers and components and...

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...

optimal subband tree structuring (SB-TS), also called wavelet packet decomposition (WPD; sometimes known as just wavelet packets or subband tree), is a wavelet...

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...