13,916 research outputs found
Speeding up weighted constraint satisfaction using redundant modeling.
Woo Hiu Chun.Thesis (M.Phil.)--Chinese University of Hong Kong, 2006.Includes bibliographical references (leaves 91-99).Abstracts in English and Chinese.Chapter 1 --- Introduction --- p.1Chapter 1.1 --- Constraint Satisfaction Problems --- p.1Chapter 1.2 --- Weighted Constraint Satisfaction Problems --- p.3Chapter 1.3 --- Redundant Modeling --- p.4Chapter 1.4 --- Motivations and Goals --- p.5Chapter 1.5 --- Outline of the Thesis --- p.6Chapter 2 --- Background --- p.8Chapter 2.1 --- Constraint Satisfaction Problems --- p.8Chapter 2.1.1 --- Backtracking Tree Search --- p.9Chapter 2.1.2 --- Local Consistencies --- p.12Chapter 2.1.3 --- Local Consistencies in Backtracking Search --- p.17Chapter 2.1.4 --- Permutation CSPs --- p.19Chapter 2.2 --- Weighted Constraint Satisfaction Problems --- p.20Chapter 2.2.1 --- Branch and Bound Search --- p.23Chapter 2.2.2 --- Local Consistencies --- p.26Chapter 2.2.3 --- Local Consistencies in Branch and Bound Search --- p.32Chapter 2.3 --- Redundant Modeling --- p.34Chapter 3 --- Generating Redundant WCSP Models --- p.37Chapter 3.1 --- Model Induction for CSPs --- p.38Chapter 3.1.1 --- Stated Constraints --- p.39Chapter 3.1.2 --- No-Double-Assignment Constraints --- p.39Chapter 3.1.3 --- At-Least-One-Assignment Constraints --- p.40Chapter 3.2 --- Generalized Model Induction for WCSPs --- p.43Chapter 4 --- Combining Mutually Redundant WCSPs --- p.47Chapter 4.1 --- Naive Approach --- p.47Chapter 4.2 --- Node Consistency Revisited --- p.51Chapter 4.2.1 --- Refining Node Consistency Definition --- p.52Chapter 4.2.2 --- Enforcing m-NC* c Algorithm --- p.55Chapter 4.3 --- Arc Consistency Revisited --- p.58Chapter 4.3.1 --- Refining Arc Consistency Definition --- p.60Chapter 4.3.2 --- Enforcing m-AC*c Algorithm --- p.62Chapter 5 --- Experiments --- p.67Chapter 5.1 --- Langford's Problem --- p.68Chapter 5.2 --- Latin Square Problem --- p.72Chapter 5.3 --- Discussion --- p.75Chapter 6 --- Related Work --- p.77Chapter 6.1 --- Soft Constraint Satisfaction Problems --- p.77Chapter 6.2 --- Other Local Consistencies in WCSPs --- p.79Chapter 6.2.1 --- Full Arc Consistency --- p.79Chapter 6.2.2 --- Pull Directional Arc Consistency --- p.81Chapter 6.2.3 --- Existential Directional Arc Consistency --- p.82Chapter 6.3 --- Redundant Modeling and Channeling Constraints --- p.83Chapter 7 --- Concluding Remarks --- p.85Chapter 7.1 --- Contributions --- p.85Chapter 7.2 --- Future Work --- p.87List of Symbols --- p.88Bibliograph
The Power of Linear Programming for Valued CSPs
A class of valued constraint satisfaction problems (VCSPs) is characterised
by a valued constraint language, a fixed set of cost functions on a finite
domain. An instance of the problem is specified by a sum of cost functions from
the language with the goal to minimise the sum. This framework includes and
generalises well-studied constraint satisfaction problems (CSPs) and maximum
constraint satisfaction problems (Max-CSPs).
Our main result is a precise algebraic characterisation of valued constraint
languages whose instances can be solved exactly by the basic linear programming
relaxation. Using this result, we obtain tractability of several novel and
previously widely-open classes of VCSPs, including problems over valued
constraint languages that are: (1) submodular on arbitrary lattices; (2)
bisubmodular (also known as k-submodular) on arbitrary finite domains; (3)
weakly (and hence strongly) tree-submodular on arbitrary trees.Comment: Corrected a few typo
Constraint-based reachability
Iterative imperative programs can be considered as infinite-state systems
computing over possibly unbounded domains. Studying reachability in these
systems is challenging as it requires to deal with an infinite number of states
with standard backward or forward exploration strategies. An approach that we
call Constraint-based reachability, is proposed to address reachability
problems by exploring program states using a constraint model of the whole
program. The keypoint of the approach is to interpret imperative constructions
such as conditionals, loops, array and memory manipulations with the
fundamental notion of constraint over a computational domain. By combining
constraint filtering and abstraction techniques, Constraint-based reachability
is able to solve reachability problems which are usually outside the scope of
backward or forward exploration strategies. This paper proposes an
interpretation of classical filtering consistencies used in Constraint
Programming as abstract domain computations, and shows how this approach can be
used to produce a constraint solver that efficiently generates solutions for
reachability problems that are unsolvable by other approaches.Comment: In Proceedings Infinity 2012, arXiv:1302.310
Maximum Persistency via Iterative Relaxed Inference with Graphical Models
We consider the NP-hard problem of MAP-inference for undirected discrete
graphical models. We propose a polynomial time and practically efficient
algorithm for finding a part of its optimal solution. Specifically, our
algorithm marks some labels of the considered graphical model either as (i)
optimal, meaning that they belong to all optimal solutions of the inference
problem; (ii) non-optimal if they provably do not belong to any solution. With
access to an exact solver of a linear programming relaxation to the
MAP-inference problem, our algorithm marks the maximal possible (in a specified
sense) number of labels. We also present a version of the algorithm, which has
access to a suboptimal dual solver only and still can ensure the
(non-)optimality for the marked labels, although the overall number of the
marked labels may decrease. We propose an efficient implementation, which runs
in time comparable to a single run of a suboptimal dual solver. Our method is
well-scalable and shows state-of-the-art results on computational benchmarks
from machine learning and computer vision.Comment: Reworked version, submitted to PAM
Aeroelastic modeling of rotor blades with spanwise variable elastic axis offset: Classic issues revisited and new formulations
In response to a systematic methodology assessment program directed to the aeroelastic stability of hingeless helicopter rotor blades, improved basic aeroelastic reformulations and new formulations relating to structural sweep were achieved. Correlational results are presented showing the substantially improved performance of the G400 aeroelastic analysis incorporating these new formulations. The formulations pertain partly to sundry solutions to classic problem areas, relating to dynamic inflow with vortex-ring state operation and basic blade kinematics, but mostly to improved physical modeling of elastic axis offset (structural sweep) in the presence of nonlinear structural twist. Specific issues addressed are an alternate modeling of the delta EI torsional excitation due to compound bending using a force integration approach, and the detailed kinematic representation of an elastically deflected point mass of a beam with both structural sweep and nonlinear twist
The power of linear programming for general-valued CSPs
Let , called the domain, be a fixed finite set and let , called
the valued constraint language, be a fixed set of functions of the form
, where different functions might have
different arity . We study the valued constraint satisfaction problem
parametrised by , denoted by VCSP. These are minimisation
problems given by variables and the objective function given by a sum of
functions from , each depending on a subset of the variables.
Finite-valued constraint languages contain functions that take on only rational
values and not infinite values.
Our main result is a precise algebraic characterisation of valued constraint
languages whose instances can be solved exactly by the basic linear programming
relaxation (BLP). For a valued constraint language , BLP is a decision
procedure for if and only if admits a symmetric fractional
polymorphism of every arity. For a finite-valued constraint language ,
BLP is a decision procedure if and only if admits a symmetric
fractional polymorphism of some arity, or equivalently, if admits a
symmetric fractional polymorphism of arity 2.
Using these results, we obtain tractability of several novel classes of
problems, including problems over valued constraint languages that are: (1)
submodular on arbitrary lattices; (2) -submodular on arbitrary finite
domains; (3) weakly (and hence strongly) tree-submodular on arbitrary trees.Comment: A full version of a FOCS'12 paper by the last two authors
(arXiv:1204.1079) and an ICALP'13 paper by the first author (arXiv:1207.7213)
to appear in SIAM Journal on Computing (SICOMP
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