4 research outputs found
Generalized Hypertree Decomposition for solving non binary CSP with compressed table constraints
International audienc
Tree Projections and Structural Decomposition Methods: Minimality and Game-Theoretic Characterization
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
Captain and Robber 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 Captain and Robber 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
Tree Projections and Structural Decomposition Methods: The Power of Local Consistency and Larger Islands of Tractability
Evaluating conjunctive queries and solving constraint satisfaction problems
are fundamental problems in database theory and artificial intelligence,
respectively. These problems are NP-hard, so that several research efforts have
been made in the literature for identifying tractable classes, known as islands
of tractability, as well as for devising clever heuristics for solving
efficiently real-world instances. Many heuristic approaches are based on
enforcing on the given instance a property called local consistency, where (in
database terms) each tuple in every query atom matches at least one tuple in
every other query atom. Interestingly, it turns out that, for many well-known
classes of queries, such as for the acyclic queries, enforcing local
consistency is even sufficient to solve the given instance correctly. However,
the precise power of such a procedure was unclear, but for some very restricted
cases. The paper provides full answers to the long-standing questions about the
precise power of algorithms based on enforcing local consistency. The classes
of instances where enforcing local consistency turns out to be a correct
query-answering procedure are however not efficiently recognizable. In fact,
the paper finally focuses on certain subclasses defined in terms of the novel
notion of greedy tree projections. These latter classes are shown to be
efficiently recognizable and strictly larger than most islands of tractability
known so far, both in the general case of tree projections and for specific
structural decomposition methods