33,292 research outputs found
Tree Projections and Constraint Optimization Problems: Fixed-Parameter Tractability and Parallel Algorithms
Tree projections provide a unifying framework to deal with most structural
decomposition methods of constraint satisfaction problems (CSPs). Within this
framework, a CSP instance is decomposed into a number of sub-problems, called
views, whose solutions are either already available or can be computed
efficiently. The goal is to arrange portions of these views in a tree-like
structure, called tree projection, which determines an efficiently solvable CSP
instance equivalent to the original one. Deciding whether a tree projection
exists is NP-hard. Solution methods have therefore been proposed in the
literature that do not require a tree projection to be given, and that either
correctly decide whether the given CSP instance is satisfiable, or return that
a tree projection actually does not exist. These approaches had not been
generalized so far on CSP extensions for optimization problems, where the goal
is to compute a solution of maximum value/minimum cost. The paper fills the
gap, by exhibiting a fixed-parameter polynomial-time algorithm that either
disproves the existence of tree projections or computes an optimal solution,
with the parameter being the size of the expression of the objective function
to be optimized over all possible solutions (and not the size of the whole
constraint formula, used in related works). Tractability results are also
established for the problem of returning the best K solutions. Finally,
parallel algorithms for such optimization problems are proposed and analyzed.
Given that the classes of acyclic hypergraphs, hypergraphs of bounded
treewidth, and hypergraphs of bounded generalized hypertree width are all
covered as special cases of the tree projection framework, the results in this
paper directly apply to these classes. These classes are extensively considered
in the CSP setting, as well as in conjunctive database query evaluation and
optimization
Constraint Design Rewriting
We propose an algebraic approach to the design and transformation of constraint networks, inspired by Architectural Design Rewriting. The approach can be understood as (i) an extension of ADR with constraints, and (ii) an application of ADR to the design of reconfigurable constraint networks. The main idea is to consider classes of constraint networks as algebras whose operators are used to denote constraint networks with terms. Constraint network transformations such as constraint propagations are specified with rewrite rules exploiting the networkās structure provided by terms
MUSE CSP: An Extension to the Constraint Satisfaction Problem
This paper describes an extension to the constraint satisfaction problem
(CSP) called MUSE CSP (MUltiply SEgmented Constraint Satisfaction Problem).
This extension is especially useful for those problems which segment into
multiple sets of partially shared variables. Such problems arise naturally in
signal processing applications including computer vision, speech processing,
and handwriting recognition. For these applications, it is often difficult to
segment the data in only one way given the low-level information utilized by
the segmentation algorithms. MUSE CSP can be used to compactly represent
several similar instances of the constraint satisfaction problem. If multiple
instances of a CSP have some common variables which have the same domains and
constraints, then they can be combined into a single instance of a MUSE CSP,
reducing the work required to apply the constraints. We introduce the concepts
of MUSE node consistency, MUSE arc consistency, and MUSE path consistency. We
then demonstrate how MUSE CSP can be used to compactly represent lexically
ambiguous sentences and the multiple sentence hypotheses that are often
generated by speech recognition algorithms so that grammar constraints can be
used to provide parses for all syntactically correct sentences. Algorithms for
MUSE arc and path consistency are provided. Finally, we discuss how to create a
MUSE CSP from a set of CSPs which are labeled to indicate when the same
variable is shared by more than a single CSP.Comment: See http://www.jair.org/ for any accompanying file
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