Graph minors. V. Excluding a planar graph
Journal of Combinatorial Theory Series B
Tree clustering for constraint networks (research note)
Artificial Intelligence
Graph rewriting: an algebraic and logic approach
Handbook of theoretical computer science (vol. B)
Solving queries by tree projections
ACM Transactions on Database Systems (TODS)
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
Conjunctive-query containment and constraint satisfaction
Journal of Computer and System Sciences - Special issue on the seventeenth ACM SIGACT-SIGMOD-SIGART symposium on principles of database systems
A comparison of structural CSP decomposition methods
Artificial Intelligence
When is the evaluation of conjunctive queries tractable?
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Query evaluation via tree-decompositions
Journal of the ACM (JACM)
Robbers, marshals, and guards: game theoretic and logical characterizations of hypertree width
Journal of Computer and System Sciences - Special issu on PODS 2001
The complexity of counting homomorphisms seen from the other side
Theoretical Computer Science
Constraint solving via fractional edge covers
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Processing queries on tree-structured data efficiently
Proceedings of the twenty-fifth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
The complexity of homomorphism and constraint satisfaction problems seen from the other side
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First-order queries on structures of bounded degree are computable with constant delay
ACM Transactions on Computational Logic (TOCL)
Algorithms for acyclic database schemes
VLDB '81 Proceedings of the seventh international conference on Very Large Data Bases - Volume 7
Tree-Related Widths of Graphs and Hypergraphs
SIAM Journal on Discrete Mathematics
A unified theory of structural tractability for constraint satisfaction problems
Journal of Computer and System Sciences
Tree-width and functional dependencies in databases
Proceedings of the twenty-seventh ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Size Bounds and Query Plans for Relational Joins
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Uniform Constraint Satisfaction Problems and Database Theory
Complexity of Constraints
Linear delay enumeration and monadic second-order logic
Discrete Applied Mathematics
Generalized hypertree decompositions: NP-hardness and tractable variants
Journal of the ACM (JACM)
Approximating fractional hypertree width
ACM Transactions on Algorithms (TALG)
Enumerating all solutions for constraint satisfaction problems
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
Tractable hypergraph properties for constraint satisfaction and conjunctive queries
Proceedings of the forty-second ACM symposium on Theory of computing
Proceedings of the twenty-ninth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Monadic datalog over finite structures of bounded treewidth
ACM Transactions on Computational Logic (TOCL)
Complexity of K-tree structured constraint satisfaction problems
AAAI'90 Proceedings of the eighth National conference on Artificial intelligence - Volume 1
Counting and enumeration problems with bounded treewidth
LPAR'10 Proceedings of the 16th international conference on Logic for programming, artificial intelligence, and reasoning
Journal of Computer and System Sciences
Enumerating all solutions of a boolean CSP by non-decreasing weight
SAT'11 Proceedings of the 14th international conference on Theory and application of satisfiability testing
Structural tractability of constraint optimization
CP'11 Proceedings of the 17th international conference on Principles and practice of constraint programming
Journal of Computer and System Sciences
MSO queries on tree decomposable structures are computable with linear delay
CSL'06 Proceedings of the 20th international conference on Computer Science Logic
Incrementally computing ordered answers of acyclic conjunctive queries
NGITS'06 Proceedings of the 6th international conference on Next Generation Information Technologies and Systems
FoIKS'12 Proceedings of the 7th international conference on Foundations of Information and Knowledge Systems
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
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
Parameterized Complexity
Theoretical Computer Science
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The problem of deciding whether CSP instances admit solutions has been deeply studied in the literature, and several structural tractability results have been derived so far. However, constraint satisfaction comes in practice as a computation problem where the focus is either on finding one solution, or on enumerating all solutions, possibly projected to some given set of output variables. The paper investigates the structural tractability of the problem of enumerating (possibly projected) solutions, where tractability means here computable with polynomial delay (WPD), since in general exponentially many solutions may be computed. A framework based on the notion of tree projection of hypergraphs is considered, which generalizes all structural decomposition methods that are based on decomposing a given instance into suitable tree-like groups of polynomial-time computable subproblems. Tractability results have been obtained both for classes of structures where output variables are part of their specification, and for classes of structures where computability WPD must be ensured for any possible set of output variables. By exhibiting dichotomies, these results are shown to be tight for classes of structures having bounded arity.