4,452 research outputs found
The Effect of Representations on Constraint Satisfaction Problems
Constraint Satisfaction is used in the solution of a wide variety of important problems such as frequency assignment, code analysis, and scheduling. It is apparent that the modelling process is key to the success of any constraint based technique, and much work has been done on the identification of good models [FJHM05]. One of the key choices made during the modelling process is the selection of a constraint representation with which to express the constraints [HS02]. Whilst practitioners will commonly use an implicit representation, most existing structural tractability results are defined for explicit representation. We address a well-known anomaly in structural tractability theory, that acyclic instances are tractable when expressed explicitly, but may not be when expressed implicitly, and show that there is a link between representation and tractability, We introduce the notion of interaction width in order to address this disconnect between theory and practice, and use this to define new tractable classes by applying existing structural tractability results to different constraint representations, We show that for a given succinct representation, a non-trivial class of instances with bounded interaction width can be transformed into an explicit representation in polynomial time 50 that existing structural tractability results may be applied, We compare our work to existing results Cor alternative succinct representutions and show that the tractable classes we have defined arc incomparable and novel, and can be used to deduce new tractable classes for SAT. 3EThOS - Electronic Theses Online ServiceGBUnited Kingdo
Tractable Combinations of Global Constraints
We study the complexity of constraint satisfaction problems involving global
constraints, i.e., special-purpose constraints provided by a solver and
represented implicitly by a parametrised algorithm. Such constraints are widely
used; indeed, they are one of the key reasons for the success of constraint
programming in solving real-world problems.
Previous work has focused on the development of efficient propagators for
individual constraints. In this paper, we identify a new tractable class of
constraint problems involving global constraints of unbounded arity. To do so,
we combine structural restrictions with the observation that some important
types of global constraint do not distinguish between large classes of
equivalent solutions.Comment: To appear in proceedings of CP'13, LNCS 8124. arXiv admin note: text
overlap with arXiv:1307.179
Structural Decompositions for Problems with Global Constraints
A wide range of problems can be modelled as constraint satisfaction problems
(CSPs), that is, a set of constraints that must be satisfied simultaneously.
Constraints can either be represented extensionally, by explicitly listing
allowed combinations of values, or implicitly, by special-purpose algorithms
provided by a solver.
Such implicitly represented constraints, known as global constraints, are
widely used; indeed, they are one of the key reasons for the success of
constraint programming in solving real-world problems. In recent years, a
variety of restrictions on the structure of CSP instances have been shown to
yield tractable classes of CSPs. However, most such restrictions fail to
guarantee tractability for CSPs with global constraints. We therefore study the
applicability of structural restrictions to instances with such constraints.
We show that when the number of solutions to a CSP instance is bounded in key
parts of the problem, structural restrictions can be used to derive new
tractable classes. Furthermore, we show that this result extends to
combinations of instances drawn from known tractable classes, as well as to CSP
instances where constraints assign costs to satisfying assignments.Comment: The final publication is available at Springer via
http://dx.doi.org/10.1007/s10601-015-9181-
Tractable Optimization Problems through Hypergraph-Based Structural Restrictions
Several variants of the Constraint Satisfaction Problem have been proposed
and investigated in the literature for modelling those scenarios where
solutions are associated with some given costs. Within these frameworks
computing an optimal solution is an NP-hard problem in general; yet, when
restricted over classes of instances whose constraint interactions can be
modelled via (nearly-)acyclic graphs, this problem is known to be solvable in
polynomial time. In this paper, larger classes of tractable instances are
singled out, by discussing solution approaches based on exploiting hypergraph
acyclicity and, more generally, structural decomposition methods, such as
(hyper)tree decompositions
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
Dichotomy Results for Fixed-Point Existence Problems for Boolean Dynamical Systems
A complete classification of the computational complexity of the fixed-point
existence problem for boolean dynamical systems, i.e., finite discrete
dynamical systems over the domain {0, 1}, is presented. For function classes F
and graph classes G, an (F, G)-system is a boolean dynamical system such that
all local transition functions lie in F and the underlying graph lies in G. Let
F be a class of boolean functions which is closed under composition and let G
be a class of graphs which is closed under taking minors. The following
dichotomy theorems are shown: (1) If F contains the self-dual functions and G
contains the planar graphs then the fixed-point existence problem for (F,
G)-systems with local transition function given by truth-tables is NP-complete;
otherwise, it is decidable in polynomial time. (2) If F contains the self-dual
functions and G contains the graphs having vertex covers of size one then the
fixed-point existence problem for (F, G)-systems with local transition function
given by formulas or circuits is NP-complete; otherwise, it is decidable in
polynomial time.Comment: 17 pages; this version corrects an error/typo in the 2008/01/24
versio
Do We Really Need Both BEKK and DCC? A Tale of Two Multivariate GARCH Models
The management and monitoring of very large portfolios of financial assets are routine for many individuals and organizations. The two most widely used models of conditional covariances and correlations in the class of multivariate GARCH models are BEKK and DCC. It is well known that BEKK suffers from the archetypal “curse of dimensionalityâ€, whereas DCC does not. It is argued in this paper that this is a misleading interpretation of the suitability of the two models for use in practice. The primary purpose of this paper is to analyze the similarities and dissimilarities between BEKK and DCC, both with and without targeting, on the basis of the structural derivation of the models, the availability of analytical forms for the sufficient conditions for existence of moments, sufficient conditions for consistency and asymptotic normality of the appropriate estimators, and computational tractability for ultra large numbers of financial assets. Based on theoretical considerations, the paper sheds light on how to discriminate between BEKK and DCC in practical applications.forecasting;conditional correlations;Hadamard models;conditional covariances;diagonal models;generalized models;scalar models;targeting
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