872 research outputs found
Pure Nash Equilibria: Hard and Easy Games
We investigate complexity issues related to pure Nash equilibria of strategic
games. We show that, even in very restrictive settings, determining whether a
game has a pure Nash Equilibrium is NP-hard, while deciding whether a game has
a strong Nash equilibrium is SigmaP2-complete. We then study practically
relevant restrictions that lower the complexity. In particular, we are
interested in quantitative and qualitative restrictions of the way each players
payoff depends on moves of other players. We say that a game has small
neighborhood if the utility function for each player depends only on (the
actions of) a logarithmically small number of other players. The dependency
structure of a game G can be expressed by a graph DG(G) or by a hypergraph
H(G). By relating Nash equilibrium problems to constraint satisfaction problems
(CSPs), we show that if G has small neighborhood and if H(G) has bounded
hypertree width (or if DG(G) has bounded treewidth), then finding pure Nash and
Pareto equilibria is feasible in polynomial time. If the game is graphical,
then these problems are LOGCFL-complete and thus in the class NC2 of highly
parallelizable problems
A Backtracking-Based Algorithm for Computing Hypertree-Decompositions
Hypertree decompositions of hypergraphs are a generalization of tree
decompositions of graphs. The corresponding hypertree-width is a measure for
the cyclicity and therefore tractability of the encoded computation problem.
Many NP-hard decision and computation problems are known to be tractable on
instances whose structure corresponds to hypergraphs of bounded
hypertree-width. Intuitively, the smaller the hypertree-width, the faster the
computation problem can be solved. In this paper, we present the new
backtracking-based algorithm det-k-decomp for computing hypertree
decompositions of small width. Our benchmark evaluations have shown that
det-k-decomp significantly outperforms opt-k-decomp, the only exact hypertree
decomposition algorithm so far. Even compared to the best heuristic algorithm,
we obtained competitive results as long as the hypergraphs are not too large.Comment: 19 pages, 6 figures, 3 table
On The Power of Tree Projections: Structural Tractability of Enumerating CSP Solutions
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 general framework based on the notion of tree
projection of hypergraphs is considered, which generalizes all known
decomposition methods. 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. These results are shown to be tight, by exhibiting
dichotomies for classes of structures having bounded arity and where the tree
decomposition method is considered
Towards Efficient Reasoning under Guarded-based Disjunctive Existential Rules
International audienceThe complete picture of the complexity of answering (unions of) conjunctive queries under the main guarded-based classes of disjunc- tive existential rules has been recently settled. It has been shown that the problem is very hard, namely 2ExpTime-complete, even for fixed sets of rules expressed in lightweight formalisms. This gives rise to the question whether its complexity can be reduced by restricting the query language. Several subclasses of conjunctive queries have been proposed with the aim of reducing the complexity of classical database problems such as query evaluation and query containment. Three of the most prominent subclasses of this kind are queries of bounded hypertree-width, queries of bounded treewidth and acyclic queries. The central objective of the present paper is to understand whether the above query languages have a positive impact on the complexity of query answering under the main guarded-based classes of disjunctive existential rules. We show that (unions of) conjunctive queries of bounded hypertree- width and of bounded treewidth do not reduce the complexity of our problem, even if we focus on predicates of bounded arity, or on fixed sets of disjunctive existential rules. Regarding acyclic queries, although our problem remains 2ExpTime-complete in general, in some relevant set- tings the complexity reduces to ExpTime-complete; in fact, this requires to bound the arity of the predicates, and for some expressive guarded- based formalisms, to fix the set of rules
High precision Monte Carlo study of the 3D XY-universality class
We present a Monte Carlo study of the two-component model on the
simple cubic lattice in three dimensions. By suitable tuning of the coupling
constant we eliminate leading order corrections to scaling. High
statistics simulations using finite size scaling techniques yield
and , where the statistical and
systematical errors are given in the first and second bracket, respectively.
These results are more precise than any previous theoretical estimate of the
critical exponents for the 3D XY universality class.Comment: 13 page
Distributed XML Design
A distributed XML document is an XML document that spans several machines. We
assume that a distribution design of the document tree is given, consisting of
an XML kernel-document T[f1,...,fn] where some leaves are "docking points" for
external resources providing XML subtrees (f1,...,fn, standing, e.g., for Web
services or peers at remote locations). The top-down design problem consists
in, given a type (a schema document that may vary from a DTD to a tree
automaton) for the distributed document, "propagating" locally this type into a
collection of types, that we call typing, while preserving desirable
properties. We also consider the bottom-up design which consists in, given a
type for each external resource, exhibiting a global type that is enforced by
the local types, again with natural desirable properties. In the article, we
lay out the fundamentals of a theory of distributed XML design, analyze
problems concerning typing issues in this setting, and study their complexity.Comment: "56 pages, 4 figures
Dyadic existential rules
In the field of ontology-based query answering, existential rules (a.k.a. tuple-generating dependencies) form an expressive Datalog-based language to specify implicit knowledge. The presence of existential quantification in rule-heads, however, makes the main reasoning tasks undecidable. To overcome this limitation, in the last two decades, a number of classes of existential rules guaranteeing the decidability of query answering have been proposed. Unfortunately, such classes are typically based on different syntactic conditions imposing the development of different ad hoc reasoners. This paper introduces a novel general condition that allows to define, systematically, from any decidable class C of existential rules, a new class called Dyadic-C that enjoys the following properties: (i) it is decidable; (ii) it generalizes C; (iii) it keeps the same data complexity as C; and (iv) it can exploit any reasoner for query answering over C. Additionally, the paper proposes a simple and elegant syntactic condition that gives rise to the class Ward+ generalizing the well-known decidable classes Shy and Ward, and being included in Dyadic-Shy
The Complexity of Reasoning for Fragments of Default Logic
Default logic was introduced by Reiter in 1980. In 1992, Gottlob classified
the complexity of the extension existence problem for propositional default
logic as \SigmaPtwo-complete, and the complexity of the credulous and
skeptical reasoning problem as SigmaP2-complete, resp. PiP2-complete.
Additionally, he investigated restrictions on the default rules, i.e.,
semi-normal default rules. Selman made in 1992 a similar approach with
disjunction-free and unary default rules. In this paper we systematically
restrict the set of allowed propositional connectives. We give a complete
complexity classification for all sets of Boolean functions in the meaning of
Post's lattice for all three common decision problems for propositional default
logic. We show that the complexity is a hexachotomy (SigmaP2-, DeltaP2-, NP-,
P-, NL-complete, trivial) for the extension existence problem, while for the
credulous and skeptical reasoning problem we obtain similar classifications
without trivial cases.Comment: Corrected versio
Polynomial combined first-order rewritings for linear and guarded existential rules
We consider the problem of ontological query answering, that is, the problem of answering a database query (typically a conjunctive query) in the presence of an ontology. This means that during the query answering process we also need to take into account the knowledge that can be inferred from the given database and ontology. Building, however, ontology-aware database systems from scratch, with sophisticated optimization techniques, is a highly non-trivial task that requires a great engineering effort. Therefore, exploiting conventional database systems is an important route towards efficient ontological query answering. Nevertheless, standard database systems are unaware of ontologies. An approach to ontological query answering that enables the use of standard database systems is the so-called polynomial combined query rewriting, originally introduced in the context of description logics: the conjunctive query q and the ontology Σ are rewritten in polynomial time into a first-order query qΣ (in a database-independent way), while the database D and the ontology Σ are rewritten in polynomial time into a new database DΣ (in a query-independent way), such that the answer to q in the presence of Σ over D coincides with the answer to qΣ over DΣ. The latter can then be computed by exploiting a conventional database system. In this work, we focus on linear and guarded existential rules, which form robust rule-based languages for modeling ontologies, and investigate the limits of polynomial combined query rewriting. In particular, we show that this type of rewriting can be successfully applied to (i) linear existential rules when the rewritten query can use the full power of first-order queries, (ii) linear existential rules when the arity of the underlying schema is fixed and the rewritten query is positive existential, namely it uses only existential quantification, conjunction, and disjunction, and (iii) guarded existential rules when the underlying schema is fixed and the rewritten query is positive existential. We can show that the above results reach the limits (under standard complexity-theoretic assumptions such as [Formula presented]) of polynomial combined query rewriting in the case of linear and guarded existential rules
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