| 词汇 | treewidth |
| 释义 | BETA Examples of treewidthtreewidth isn’t in the Cambridge Dictionary yet. You can help! It is also a 3-tree, and therefore it has treewidth 3. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Treewidth is commonly used as a parameter in the parameterized complexity analysis of graph algorithms. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. However, there exist graphs with bounded degeneracy and unbounded treewidth, such as the grid graphs. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. In this definition, the size of the largest set is diminished by one in order to make the treewidth of a tree equal to one. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Thus, in graphs of bounded treewidth, the maximum independent set problem may be solved in linear time. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Therefore, the degeneracy is at most equal to the treewidth and at most equal to the pathwidth. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. This dynamic programming approach is used in machine learning via the junction tree algorithm for belief propagation in graphs of bounded treewidth. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Since path-decompositions are a special case of tree-decompositions, the pathwidth of any graph is greater than or equal to its treewidth. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. The graphs with treewidth at most "k" are also called partial "k" -trees; many other well-studied graph families also have bounded treewidth. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. A connected graph with at least two vertices has treewidth 1 if and only if it is a tree. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Alternatively, the pathwidth may be defined from interval graphs analogously to the definition of treewidth from chordal graphs. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Specifically, a weighted constraint satisfaction problem can be solved in time exponential only in the treewidth of its variable-interaction graph (constraint network). From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. It is also possible for a class of graphs that is not closed under minors to have bounded local treewidth. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. A tree has treewidth one by the same reasoning as for complete graphs (namely, it is chordal, and has maximum clique size two). From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. All of these methods have complexity that is exponential in the network's treewidth. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. The strong exponential time hypothesis leads to tight bounds on the parameterized complexity of several graph problems on graphs of bounded treewidth. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Pathwidth and path-decompositions are closely analogous to treewidth and tree decompositions. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. As a consequence, the pathwidth of a graph is always at least as large as its treewidth, but it can only be larger by a logarithmic factor. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. |
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