Tree clustering for constraint networks (research note)
Artificial Intelligence
Solving queries by tree projections
ACM Transactions on Database Systems (TODS)
Graph searching and a min-max theorem for tree-width
Journal of Combinatorial Theory Series B
A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth
SIAM Journal on Computing
Acyclic hypergraph projections
Journal of Algorithms
Degrees of acyclicity for hypergraphs and relational database schemes
Journal of the ACM (JACM)
Syntactic Characterization of Tree Database Schemas
Journal of the ACM (JACM)
A comparison of structural CSP decomposition methods
Artificial Intelligence
Robbers, marshals, and guards: game theoretic and logical characterizations of hypertree width
Journal of Computer and System Sciences - Special issu on PODS 2001
Constraint solving via fractional edge covers
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
The complexity of homomorphism and constraint satisfaction problems seen from the other side
Journal of the ACM (JACM)
Hypertree width and related hypergraph invariants
European Journal of Combinatorics
A unified theory of structural tractability for constraint satisfaction problems
Journal of Computer and System Sciences
Marshals, monotone marshals, and hypertree-width
Journal of Graph Theory
Tree Projections: Hypergraph Games and Minimality
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part I
Generalized hypertree decompositions: NP-hardness and tractable variants
Journal of the ACM (JACM)
Backtracking procedures for hypertree, hyperspread and connected hypertree decomposition of CSPs
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
Proceedings of the twenty-ninth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Complexity of K-tree structured constraint satisfaction problems
AAAI'90 Proceedings of the eighth National conference on Artificial intelligence - Volume 1
Connected treewidth and connected graph searching
LATIN'06 Proceedings of the 7th Latin American conference on Theoretical Informatics
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
Tractable Hypergraph Properties for Constraint Satisfaction and Conjunctive Queries
Journal of the ACM (JACM)
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Tree projections provide a mathematical framework that encompasses all the various (purely) structural decomposition methods that have been proposed in the literature to single out classes of nearly-acyclic (hyper)graphs, such as the tree decomposition method, which is the most powerful decomposition method on graphs, and the (generalized) hypertree decomposition method, which is its natural counterpart on arbitrary hypergraphs. The paper analyzes this framework, by focusing in particular on ''minimal'' tree projections, that is, on tree projections without useless redundancies. First, it is shown that minimal tree projections enjoy a number of properties that are usually required for normal form decompositions in various structural decomposition methods. In particular, they enjoy the same kind of connection properties as (minimal) tree decompositions of graphs, with the result being tight in the light of the negative answer that is provided to the open question about whether they enjoy a slightly stronger notion of connection property, defined to speed-up the computation of hypertree decompositions. Second, it is shown that tree projections admit a natural game-theoretic characterization in terms of the Robber and Captain game. In this game, as for the Robber and Cops game characterizing tree decompositions, the existence of winning strategies implies the existence of monotone ones. As a special case, the Robber and Captain game can be used to characterize the generalized hypertree decomposition method, where such a game-theoretic characterization was missing and asked for. Besides their theoretical interest, these results have immediate algorithmic applications both for the general setting and for structural decomposition methods that can be recast in terms of tree projections.