6,945 research outputs found
The alldifferent Constraint: A Survey
The constraint of difference is known to the constraint programming community
since Lauriere introduced Alice in 1978. Since then, several solving strategies
have been designed for this constraint. In this paper we give both a practical
overview and an abstract comparison of these different strategies.Comment: 12 pages, 3 figures, paper accepted at the 6th Annual workshop of the
ERCIM Working Group on Constraint
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
Property-Driven Fence Insertion using Reorder Bounded Model Checking
Modern architectures provide weaker memory consistency guarantees than
sequential consistency. These weaker guarantees allow programs to exhibit
behaviours where the program statements appear to have executed out of program
order. Fortunately, modern architectures provide memory barriers (fences) to
enforce the program order between a pair of statements if needed. Due to the
intricate semantics of weak memory models, the placement of fences is
challenging even for experienced programmers. Too few fences lead to bugs
whereas overuse of fences results in performance degradation. This motivates
automated placement of fences. Tools that restore sequential consistency in the
program may insert more fences than necessary for the program to be correct.
Therefore, we propose a property-driven technique that introduces
"reorder-bounded exploration" to identify the smallest number of program
locations for fence placement. We implemented our technique on top of CBMC;
however, in principle, our technique is generic enough to be used with any
model checker. Our experimental results show that our technique is faster and
solves more instances of relevant benchmarks as compared to earlier approaches.Comment: 18 pages, 3 figures, 4 algorithms. Version change reason : new set of
results and publication ready version of FM 201
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
Incremental Cardinality Constraints for MaxSAT
Maximum Satisfiability (MaxSAT) is an optimization variant of the Boolean
Satisfiability (SAT) problem. In general, MaxSAT algorithms perform a
succession of SAT solver calls to reach an optimum solution making extensive
use of cardinality constraints. Many of these algorithms are non-incremental in
nature, i.e. at each iteration the formula is rebuilt and no knowledge is
reused from one iteration to another. In this paper, we exploit the knowledge
acquired across iterations using novel schemes to use cardinality constraints
in an incremental fashion. We integrate these schemes with several MaxSAT
algorithms. Our experimental results show a significant performance boost for
these algo- rithms as compared to their non-incremental counterparts. These
results suggest that incremental cardinality constraints could be beneficial
for other constraint solving domains.Comment: 18 pages, 4 figures, 1 table. Final version published in Principles
and Practice of Constraint Programming (CP) 201
Mapping constrained optimization problems to quantum annealing with application to fault diagnosis
Current quantum annealing (QA) hardware suffers from practical limitations
such as finite temperature, sparse connectivity, small qubit numbers, and
control error. We propose new algorithms for mapping boolean constraint
satisfaction problems (CSPs) onto QA hardware mitigating these limitations. In
particular we develop a new embedding algorithm for mapping a CSP onto a
hardware Ising model with a fixed sparse set of interactions, and propose two
new decomposition algorithms for solving problems too large to map directly
into hardware.
The mapping technique is locally-structured, as hardware compatible Ising
models are generated for each problem constraint, and variables appearing in
different constraints are chained together using ferromagnetic couplings. In
contrast, global embedding techniques generate a hardware independent Ising
model for all the constraints, and then use a minor-embedding algorithm to
generate a hardware compatible Ising model. We give an example of a class of
CSPs for which the scaling performance of D-Wave's QA hardware using the local
mapping technique is significantly better than global embedding.
We validate the approach by applying D-Wave's hardware to circuit-based
fault-diagnosis. For circuits that embed directly, we find that the hardware is
typically able to find all solutions from a min-fault diagnosis set of size N
using 1000N samples, using an annealing rate that is 25 times faster than a
leading SAT-based sampling method. Further, we apply decomposition algorithms
to find min-cardinality faults for circuits that are up to 5 times larger than
can be solved directly on current hardware.Comment: 22 pages, 4 figure
Compactly generating all satisfying truth assignments of a Horn formula
As instance of an overarching principle of exclusion an algorithm is
presented that compactly (thus not one by one) generates all models of a Horn
formula. The principle of exclusion can be adapted to generate only the models
of weight . We compare and contrast it with constraint programming,
integer programming, and binary decision diagrams.Comment: Considerably improves upon the readibility of the previous versio
Breaking Instance-Independent Symmetries In Exact Graph Coloring
Code optimization and high level synthesis can be posed as constraint
satisfaction and optimization problems, such as graph coloring used in register
allocation. Graph coloring is also used to model more traditional CSPs relevant
to AI, such as planning, time-tabling and scheduling. Provably optimal
solutions may be desirable for commercial and defense applications.
Additionally, for applications such as register allocation and code
optimization, naturally-occurring instances of graph coloring are often small
and can be solved optimally. A recent wave of improvements in algorithms for
Boolean satisfiability (SAT) and 0-1 Integer Linear Programming (ILP) suggests
generic problem-reduction methods, rather than problem-specific heuristics,
because (1) heuristics may be upset by new constraints, (2) heuristics tend to
ignore structure, and (3) many relevant problems are provably inapproximable.
Problem reductions often lead to highly symmetric SAT instances, and
symmetries are known to slow down SAT solvers. In this work, we compare several
avenues for symmetry breaking, in particular when certain kinds of symmetry are
present in all generated instances. Our focus on reducing CSPs to SAT allows us
to leverage recent dramatic improvement in SAT solvers and automatically
benefit from future progress. We can use a variety of black-box SAT solvers
without modifying their source code because our symmetry-breaking techniques
are static, i.e., we detect symmetries and add symmetry breaking predicates
(SBPs) during pre-processing.
An important result of our work is that among the types of
instance-independent SBPs we studied and their combinations, the simplest and
least complete constructions are the most effective. Our experiments also
clearly indicate that instance-independent symmetries should mostly be
processed together with instance-specific symmetries rather than at the
specification level, contrary to what has been suggested in the literature
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