Journal ArticleDOI
Easy problems for tree-decomposable graphs
TLDR
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.About:
This article is published in Journal of Algorithms.The article was published on 1991-04-01. It has received 940 citations till now. The article focuses on the topics: Courcelle's theorem & Chordal graph.read more
Citations
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Journal 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 at most some constant $k$ and finds a tree-decomposition of G withtreewidth at most k.
Book
Parameterized Algorithms
Marek Cygan,Fedor V. Fomin,Lukasz Kowalik,Daniel Lokshtanov,Dániel Marx,Marcin Pilipczuk,Michał Pilipczuk,Saket Saurabh +7 more
TL;DR: This comprehensive textbook presents a clean and coherent account of most fundamental tools and techniques in Parameterized Algorithms and is a self-contained guide to the area, providing a toolbox of algorithmic techniques.
Journal ArticleDOI
The Computational Structure of Monotone Monadic SNP and Constraint Satisfaction: A Study through Datalog and Group Theory
Tomás Feder,Moshe Y. Vardi +1 more
TL;DR: This paper isolates a class (of problems specified by) "monotone monadic SNP without inequality" which may exhibit a dichotomy, and explains the placing of all these restrictions by showing, essentially using Ladner's theorem, that classes obtained by using only two of the above three restrictions do not show this dichotomy.
Journal ArticleDOI
Linear Time Solvable Optimization Problems on Graphs of Bounded Clique-Width
TL;DR: It is proved that this is also the case for graphs of clique-width at most k, where this complexity measure is associated with hierarchical decompositions of another type, and where logical formulas are no longer allowed to use edge set quantifications.
Journal Article
A tourist guide through treewidth
TL;DR: 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.
References
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Book
The Design and Analysis of Computer Algorithms
Alfred V. Aho,John E. Hopcroft +1 more
TL;DR: This text introduces the basic data structures and programming techniques often used in efficient algorithms, and covers use of lists, push-down stacks, queues, trees, and graphs.
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.
Book
Logical Foundations of Artificial Intelligence
TL;DR: Typographical Conventions 1 Introduction 1 Bibliographical and Historical Remarks Exercises 2 Declarative Knowledge 2.1 Conceptualization 2.2 Predicate Calculus 2.3 Semantics 2.4 Blocks World Example 2.5 Circuits 2.6 Algebraic Examples 2.7 List Examples 1.9 Specialized Languages 2.8 Reasoning with Uncertain Reasoning 3.1 Probabilities of Sentences 3.4 Provability 3.5 Proving Provability