Open AccessJournal Article
A tourist guide through treewidth
TLDR
A short overview of recent results in algorithmic graph theory that deal with the notions treewidth and pathwidth can be found in this paper, where the authors discuss algorithms that find tree-decomposition, algorithms that use treedecompositions to solve hard problems efficiently, graph minor theory, and some applications.Abstract:
A short overview is given of many recent results in algorithmic graph theory that deal with the notions treewidth, and pathwidth. We discuss algorithms that find tree-decompositions, algorithms that use tree-decompositions to solve hard problems efficiently, graph minor theory, and some applications. The paper contains an extensive bibliography.read more
Citations
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Pattern Recognition and Machine Learning
TL;DR: Probability distributions of linear models for regression and classification are given in this article, along with a discussion of combining models and combining models in the context of machine learning and classification.
Book
Graphical Models, Exponential Families, and Variational Inference
TL;DR: The variational approach provides a complementary alternative to Markov chain Monte Carlo as a general source of approximation methods for inference in large-scale statistical models.
Journal ArticleDOI
A partial k -arboretum of graphs with bounded treewidth
TL;DR: This survey paper wants to give an overview of many classes of graphs that can be seen to have a uniform upper bound on the treewidth of graphs in the class.
Proceedings ArticleDOI
A linear time algorithm for finding tree-decompositions of small treewidth
TL;DR: Every minor-closed class of graphs that does not contain all planar graphs has a linear time recognition algorithm that determines whether the treewidth of G is at most k, and if so, finds a treedecomposition of G withtreewidth at mostK.
Journal ArticleDOI
A survey of graph layout problems
TL;DR: A complete view of the current state of the art with respect to layout problems from an algorithmic point of view is presented.
References
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Journal ArticleDOI
Graph minors. II: Algorithmic aspects of tree-width
Neil Robertson,Paul Seymour +1 more
TL;DR: An invariant of graphs called the tree-width is introduced, and used to obtain a polynomially bounded algorithm to test if a graph has a subgraph contractible to H, where H is any fixed planar graph.
Journal ArticleDOI
The monadic second-order logic of graphs. I. recognizable sets of finite graphs
TL;DR: Every set of finite graphs, that is definable in monadic second-order logic is recognizable, but not vice versa, and the monadicsecond-order theory of a context-free set of graphs is decidable.
Journal ArticleDOI
Graph minors. XIII: the disjoint paths problem
Neil Robertson,Paul Seymour +1 more
TL;DR: An algorithm, which for fixed k ≥ 0 has running time O (| V(G) | 3 ), to solve the following problem: given a graph G and k pairs of vertices of G, decide if there are k mutually vertex-disjoint paths of G joining the pairs.
Journal ArticleDOI
Complexity of finding embeddings in a k -tree
TL;DR: This work determines the complexity status of two problems related to finding the smallest number k such that a given graph is a partial k-tree and presents an algorithm with polynomially bounded (but exponential in k) worst case time complexity.
Journal ArticleDOI
Easy problems for tree-decomposable graphs
TL;DR: Using a variation of the interpretability concept, it is shown that all graph properties definable in monadic second-order logic with quantification over vertex and edge sets can be decided in linear time for classes of graphs of fixed bounded treewidth given a tree-decomposition.