1,704 research outputs found
SAT vs CSP: a commentary
In 2000, I published a relatively comprehensive study of mappings between
propositional satisfiability (SAT) and constraint satisfaction problems (CSPs)
[Wal00]. I analysed four different mappings of SAT problems into CSPs, and two
of CSPs into SAT problems. For each mapping, I compared the impact of achieving
arc-consistency on the CSP with unit propagation on the corresponding SAT
problems, and lifted these results to CSP algorithms that maintain (some level
of ) arc-consistency during search like FC and MAC, and to the Davis- Putnam
procedure (which performs unit propagation at each search node). These results
helped provide some insight into the relationship between propositional
satisfiability and constraint satisfaction that set the scene for an important
and valuable body of work that followed. I discuss here what prompted the
paper, and what followed.Comment: See https://freuder.wordpress.com/cp-anniversary-project
Decentralized Constraint Satisfaction
We show that several important resource allocation problems in wireless
networks fit within the common framework of Constraint Satisfaction Problems
(CSPs). Inspired by the requirements of these applications, where variables are
located at distinct network devices that may not be able to communicate but may
interfere, we define natural criteria that a CSP solver must possess in order
to be practical. We term these algorithms decentralized CSP solvers. The best
known CSP solvers were designed for centralized problems and do not meet these
criteria. We introduce a stochastic decentralized CSP solver and prove that it
will find a solution in almost surely finite time, should one exist, also
showing it has many practically desirable properties. We benchmark the
algorithm's performance on a well-studied class of CSPs, random k-SAT,
illustrating that the time the algorithm takes to find a satisfying assignment
is competitive with stochastic centralized solvers on problems with order a
thousand variables despite its decentralized nature. We demonstrate the
solver's practical utility for the problems that motivated its introduction by
using it to find a non-interfering channel allocation for a network formed from
data from downtown Manhattan
Short Portfolio Training for CSP Solving
Many different approaches for solving Constraint Satisfaction Problems (CSPs)
and related Constraint Optimization Problems (COPs) exist. However, there is no
single solver (nor approach) that performs well on all classes of problems and
many portfolio approaches for selecting a suitable solver based on simple
syntactic features of the input CSP instance have been developed. In this paper
we first present a simple portfolio method for CSP based on k-nearest neighbors
method. Then, we propose a new way of using portfolio systems --- training them
shortly in the exploitation time, specifically for the set of instances to be
solved and using them on that set. Thorough evaluation has been performed and
has shown that the approach yields good results. We evaluated several machine
learning techniques for our portfolio. Due to its simplicity and efficiency,
the selected k-nearest neighbors method is especially suited for our short
training approach and it also yields the best results among the tested methods.
We also confirm that our approach yields good results on SAT domain.Comment: 21 page
Translation-based Constraint Answer Set Solving
We solve constraint satisfaction problems through translation to answer set
programming (ASP). Our reformulations have the property that unit-propagation
in the ASP solver achieves well defined local consistency properties like arc,
bound and range consistency. Experiments demonstrate the computational value of
this approach.Comment: Self-archived version for IJCAI'11 Best Paper Track submissio
Streamlining Variational Inference for Constraint Satisfaction Problems
Several algorithms for solving constraint satisfaction problems are based on
survey propagation, a variational inference scheme used to obtain approximate
marginal probability estimates for variable assignments. These marginals
correspond to how frequently each variable is set to true among satisfying
assignments, and are used to inform branching decisions during search; however,
marginal estimates obtained via survey propagation are approximate and can be
self-contradictory. We introduce a more general branching strategy based on
streamlining constraints, which sidestep hard assignments to variables. We show
that streamlined solvers consistently outperform decimation-based solvers on
random k-SAT instances for several problem sizes, shrinking the gap between
empirical performance and theoretical limits of satisfiability by 16.3% on
average for k=3,4,5,6.Comment: NeurIPS 201
Constraint Satisfaction by Survey Propagation
Survey Propagation is an algorithm designed for solving typical instances of
random constraint satisfiability problems. It has been successfully tested on
random 3-SAT and random graph 3-coloring, in the hard region
of the parameter space. Here we provide a generic formalism which applies to a
wide class of discrete Constraint Satisfaction Problems.Comment: 8 pages, 5 figure
A Bayesian Approach to Tackling Hard Computational Problems
We are developing a general framework for using learned Bayesian models for
decision-theoretic control of search and reasoningalgorithms. We illustrate the
approach on the specific task of controlling both general and domain-specific
solvers on a hard class of structured constraint satisfaction problems. A
successful strategyfor reducing the high (and even infinite) variance in
running time typically exhibited by backtracking search algorithms is to cut
off and restart the search if a solution is not found within a certainamount of
time. Previous work on restart strategies have employed fixed cut off values.
We show how to create a dynamic cut off strategy by learning a Bayesian model
that predicts the ultimate length of a trial based on observing the early
behavior of the search algorithm. Furthermore, we describe the general
conditions under which a dynamic restart strategy can outperform the
theoretically optimal fixed strategy.Comment: Appears in Proceedings of the Seventeenth Conference on Uncertainty
in Artificial Intelligence (UAI2001
Is SP BP?
The Survey Propagation (SP) algorithm for solving -SAT problems has been
shown recently as an instance of the Belief Propagation (BP) algorithm. In this
paper, we show that for general constraint-satisfaction problems, SP may not be
reducible from BP. We also establish the conditions under which such a
reduction is possible. Along our development, we present a unification of the
existing SP algorithms in terms of a probabilistically interpretable iterative
procedure -- weighted Probabilistic Token Passing.Comment: 77 page double-spaced single-column submitted version to IEEE
Transactions on Information Theor
Exploiting the Pruning Power of Strong Local Consistencies Through Parallelization
Local consistencies stronger than arc consistency have received a lot of
attention since the early days of CSP research. %because of the strong pruning
they can achieve. However, they have not been widely adopted by CSP solvers.
This is because applying such consistencies can sometimes result in
considerably smaller search tree sizes and therefore in important speed-ups,
but in other cases the search space reduction may be small, causing severe run
time penalties. Taking advantage of recent advances in parallelization, we
propose a novel approach for the application of strong local consistencies
(SLCs) that can improve their performance by largely preserving the speed-ups
they offer in cases where they are successful, and eliminating the run time
penalties in cases where they are unsuccessful. This approach is presented in
the form of two search algorithms. Both algorithms consist of a master search
process, which is a typical CSP solver, and a number of slave processes, with
each one implementing a SLC method. The first algorithm runs the different SLCs
synchronously at each node of the search tree explored in the master process,
while the second one can run them asynchronously at different nodes of the
search tree. Experimental results demonstrate the benefits of the proposed
method
Aspartame: Solving Constraint Satisfaction Problems with Answer Set Programming
Encoding finite linear CSPs as Boolean formulas and solving them by using
modern SAT solvers has proven to be highly effective, as exemplified by the
award-winning sugar system. We here develop an alternative approach based on
ASP. This allows us to use first-order encodings providing us with a high
degree of flexibility for easy experimentation with different implementations.
The resulting system aspartame re-uses parts of sugar for parsing and
normalizing CSPs. The obtained set of facts is then combined with an ASP
encoding that can be grounded and solved by off-the-shelf ASP systems. We
establish the competitiveness of our approach by empirically contrasting
aspartame and sugar.Comment: Proceedings of Answer Set Programming and Other Computing Paradigms
(ASPOCP 2013), 6th International Workshop, August 25, 2013, Istanbul, Turke
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