Easy problems for tree-decomposable graphs
Journal of Algorithms
Graph rewriting: an algebraic and logic approach
Handbook of theoretical computer science (vol. B)
Monadic second-order evaluations on tree-decomposable graphs
Theoretical Computer Science - Special issue on selected papers of the International Workshop on Computing by Graph Transformation, Bordeaux, France, March 21–23, 1991
A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth
SIAM Journal on Computing
Data Structures and Algorithms
Data Structures and Algorithms
Machine-Independent Characterizations and Complete Problems for Deterministic Linear Time
SIAM Journal on Computing
Query evaluation via tree-decompositions
Journal of the ACM (JACM)
Graph properties checkable in linear time in the number of vertices
Journal of Computer and System Sciences
First-order queries on structures of bounded degree are computable with constant delay
ACM Transactions on Computational Logic (TOCL)
Elements of Finite Model Theory
Elements of Finite Model Theory
Parameterized Complexity
Polynomial time fragments of XPath with variables
Proceedings of the twenty-sixth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Linear delay enumeration and monadic second-order logic
Discrete Applied Mathematics
Computing representations of matroids of bounded branch-width
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
Compact representation for answer sets of n-ary regular queries
Theoretical Computer Science
Database theory: query languages
Algorithms and theory of computation handbook
Efficient enumeration for conjunctive queries over x-underbar structures
CSL'10/EACSL'10 Proceedings of the 24th international conference/19th annual conference on Computer science logic
Counting and enumeration problems with bounded treewidth
LPAR'10 Proceedings of the 16th international conference on Logic for programming, artificial intelligence, and reasoning
First-Order queries over one unary function
CSL'06 Proceedings of the 20th international conference on Computer Science Logic
On acyclic conjunctive queries and constant delay enumeration
CSL'07/EACSL'07 Proceedings of the 21st international conference, and Proceedings of the 16th annuall conference on Computer Science Logic
Enumerating with constant delay the answers to a query
Proceedings of the 16th International Conference on Database Theory
Enumeration of first-order queries on classes of structures with bounded expansion
Proceedings of the 32nd symposium on Principles of database systems
Enumeration of monadic second-order queries on trees
ACM Transactions on Computational Logic (TOCL)
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Linear-Delaylin is the class of enumeration problems computable in two steps: the first step is a precomputation in linear time in the size of the input and the second step computes successively all the solutions with a delay between two consecutive solutions y1 and y2 that is linear in |y2|. We prove that evaluating a fixed monadic second order (MSO) query $\varphi(\bar{X})$ (i.e. computing all the tuples that satisfy the MSO formula) in a binary tree is a Linear-Delaylin problem. More precisely, we show that given a binary tree T and a tree automaton Γ representing an MSO query $\varphi(\bar{X})$, we can evaluate Γ on T with a preprocessing in time and space complexity O(|Γ|3|T|) and an enumeration phase with a delay O(|S|) and space O(max|S|) where |S| is the size of the next solution and max|S| is the size of the largest solution. We introduce a new kind of algorithm with nice complexity properties for some algebraic operations on enumeration problems. In addition, we extend the precomputation (with the same complexity) such that the ith (with respect to a certain order) solution S is produced directly in time O(|S|log(|T|)). Finally, we generalize these results to bounded treewidth structures.