5,489 research outputs found
Solving Set Constraint Satisfaction Problems using ROBDDs
In this paper we present a new approach to modeling finite set domain
constraint problems using Reduced Ordered Binary Decision Diagrams (ROBDDs). We
show that it is possible to construct an efficient set domain propagator which
compactly represents many set domains and set constraints using ROBDDs. We
demonstrate that the ROBDD-based approach provides unprecedented flexibility in
modeling constraint satisfaction problems, leading to performance improvements.
We also show that the ROBDD-based modeling approach can be extended to the
modeling of integer and multiset constraint problems in a straightforward
manner. Since domain propagation is not always practical, we also show how to
incorporate less strict consistency notions into the ROBDD framework, such as
set bounds, cardinality bounds and lexicographic bounds consistency. Finally,
we present experimental results that demonstrate the ROBDD-based solver
performs better than various more conventional constraint solvers on several
standard set constraint problems
Conjunctions of Among Constraints
Many existing global constraints can be encoded as a conjunction of among
constraints. An among constraint holds if the number of the variables in its
scope whose value belongs to a prespecified set, which we call its range, is
within some given bounds. It is known that domain filtering algorithms can
benefit from reasoning about the interaction of among constraints so that
values can be filtered out taking into consideration several among constraints
simultaneously. The present pa- per embarks into a systematic investigation on
the circumstances under which it is possible to obtain efficient and complete
domain filtering algorithms for conjunctions of among constraints. We start by
observing that restrictions on both the scope and the range of the among
constraints are necessary to obtain meaningful results. Then, we derive a
domain flow-based filtering algorithm and present several applications. In
particular, it is shown that the algorithm unifies and generalizes several
previous existing results.Comment: 15 pages plus appendi
Efficient Constellation-Based Map-Merging for Semantic SLAM
Data association in SLAM is fundamentally challenging, and handling ambiguity
well is crucial to achieve robust operation in real-world environments. When
ambiguous measurements arise, conservatism often mandates that the measurement
is discarded or a new landmark is initialized rather than risking an incorrect
association. To address the inevitable `duplicate' landmarks that arise, we
present an efficient map-merging framework to detect duplicate constellations
of landmarks, providing a high-confidence loop-closure mechanism well-suited
for object-level SLAM. This approach uses an incrementally-computable
approximation of landmark uncertainty that only depends on local information in
the SLAM graph, avoiding expensive recovery of the full system covariance
matrix. This enables a search based on geometric consistency (GC) (rather than
full joint compatibility (JC)) that inexpensively reduces the search space to a
handful of `best' hypotheses. Furthermore, we reformulate the commonly-used
interpretation tree to allow for more efficient integration of clique-based
pairwise compatibility, accelerating the branch-and-bound max-cardinality
search. Our method is demonstrated to match the performance of full JC methods
at significantly-reduced computational cost, facilitating robust object-based
loop-closure over large SLAM problems.Comment: Accepted to IEEE International Conference on Robotics and Automation
(ICRA) 201
Guarantees and Limits of Preprocessing in Constraint Satisfaction and Reasoning
We present a first theoretical analysis of the power of polynomial-time
preprocessing for important combinatorial problems from various areas in AI. We
consider problems from Constraint Satisfaction, Global Constraints,
Satisfiability, Nonmonotonic and Bayesian Reasoning under structural
restrictions. All these problems involve two tasks: (i) identifying the
structure in the input as required by the restriction, and (ii) using the
identified structure to solve the reasoning task efficiently. We show that for
most of the considered problems, task (i) admits a polynomial-time
preprocessing to a problem kernel whose size is polynomial in a structural
problem parameter of the input, in contrast to task (ii) which does not admit
such a reduction to a problem kernel of polynomial size, subject to a
complexity theoretic assumption. As a notable exception we show that the
consistency problem for the AtMost-NValue constraint admits a polynomial kernel
consisting of a quadratic number of variables and domain values. Our results
provide a firm worst-case guarantees and theoretical boundaries for the
performance of polynomial-time preprocessing algorithms for the considered
problems.Comment: arXiv admin note: substantial text overlap with arXiv:1104.2541,
arXiv:1104.556
Inference with Constrained Hidden Markov Models in PRISM
A Hidden Markov Model (HMM) is a common statistical model which is widely
used for analysis of biological sequence data and other sequential phenomena.
In the present paper we show how HMMs can be extended with side-constraints and
present constraint solving techniques for efficient inference. Defining HMMs
with side-constraints in Constraint Logic Programming have advantages in terms
of more compact expression and pruning opportunities during inference.
We present a PRISM-based framework for extending HMMs with side-constraints
and show how well-known constraints such as cardinality and all different are
integrated. We experimentally validate our approach on the biologically
motivated problem of global pairwise alignment
Solving finite-domain linear constraints in presence of the
In this paper, we investigate the possibility of improvement of the
widely-used filtering algorithm for the linear constraints in constraint
satisfaction problems in the presence of the alldifferent constraints. In many
cases, the fact that the variables in a linear constraint are also constrained
by some alldifferent constraints may help us to calculate stronger bounds of
the variables, leading to a stronger constraint propagation. We propose an
improved filtering algorithm that targets such cases. We provide a detailed
description of the proposed algorithm and prove its correctness. We evaluate
the approach on five different problems that involve combinations of the linear
and the alldifferent constraints. We also compare our algorithm to other
relevant approaches. The experimental results show a great potential of the
proposed improvement.Comment: 28 pages, 2 figure
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
Symmetry Breaking Using Value Precedence
We present a comprehensive study of the use of value precedence constraints
to break value symmetry. We first give a simple encoding of value precedence
into ternary constraints that is both efficient and effective at breaking
symmetry. We then extend value precedence to deal with a number of
generalizations like wreath value and partial interchangeability. We also show
that value precedence is closely related to lexicographical ordering. Finally,
we consider the interaction between value precedence and symmetry breaking
constraints for variable symmetries.Comment: 17th European Conference on Artificial Intelligenc
- …