1,392 research outputs found
Efficient structural symmetry breaking for constraint satisfaction problems
Symmetry breaking for constraint satisfaction
problems (CSPs) has attracted considerable attention
in recent years. Various general schemes have been proposed to eliminate symmetries. In general, these schemes may take exponential space or time to eliminate all the symmetries. We identify several classes of CSPs that encompass many practical problems and for which symmetry breaking for various forms of value and variable interchangeability is tractable using dedicated search procedures or symmetry-breaking constraints that allow nogoods and their symmetrically equivalent solutions to be stored and checked efficiently
Symmetry within Solutions
We define the concept of an internal symmetry. This is a symmety within a
solution of a constraint satisfaction problem. We compare this to solution
symmetry, which is a mapping between different solutions of the same problem.
We argue that we may be able to exploit both types of symmetry when finding
solutions. We illustrate the potential of exploiting internal symmetries on two
benchmark domains: Van der Waerden numbers and graceful graphs. By identifying
internal symmetries we are able to extend the state of the art in both cases.Comment: AAAI 2010, Proceedings of Twenty-Fourth AAAI Conference on Artificial
Intelligenc
Symmetries in planning problems
Symmetries arise in planning in a variety of ways. This paper describes the ways that symmetry aises most naturally in planning problems and reviews the approaches that have been applied to exploitation of symmetry in order to reduce search for plans. It then introduces some extensions to the use of symmetry in planning before moving on to consider how the exploitation of symmetry in planning might be generalised to offer new approaches to exploitation of symmetry in other combinatorial search problems
Generating and Sampling Orbits for Lifted Probabilistic Inference
A key goal in the design of probabilistic inference algorithms is identifying
and exploiting properties of the distribution that make inference tractable.
Lifted inference algorithms identify symmetry as a property that enables
efficient inference and seek to scale with the degree of symmetry of a
probability model. A limitation of existing exact lifted inference techniques
is that they do not apply to non-relational representations like factor graphs.
In this work we provide the first example of an exact lifted inference
algorithm for arbitrary discrete factor graphs. In addition we describe a
lifted Markov-Chain Monte-Carlo algorithm that provably mixes rapidly in the
degree of symmetry of the distribution
Solving Graph Coloring Problems with Abstraction and Symmetry
This paper introduces a general methodology, based on abstraction and
symmetry, that applies to solve hard graph edge-coloring problems and
demonstrates its use to provide further evidence that the Ramsey number
. The number is often presented as the unknown Ramsey
number with the best chances of being found "soon". Yet, its precise value has
remained unknown for more than 50 years. We illustrate our approach by showing
that: (1) there are precisely 78{,}892 Ramsey colorings; and (2)
if there exists a Ramsey coloring then it is (13,8,8) regular.
Specifically each node has 13 edges in the first color, 8 in the second, and 8
in the third. We conjecture that these two results will help provide a proof
that no Ramsey coloring exists implying that
Symmetry Breaking for Answer Set Programming
In the context of answer set programming, this work investigates symmetry
detection and symmetry breaking to eliminate symmetric parts of the search
space and, thereby, simplify the solution process. We contribute a reduction of
symmetry detection to a graph automorphism problem which allows to extract
symmetries of a logic program from the symmetries of the constructed coloured
graph. We also propose an encoding of symmetry-breaking constraints in terms of
permutation cycles and use only generators in this process which implicitly
represent symmetries and always with exponential compression. These ideas are
formulated as preprocessing and implemented in a completely automated flow that
first detects symmetries from a given answer set program, adds
symmetry-breaking constraints, and can be applied to any existing answer set
solver. We demonstrate computational impact on benchmarks versus direct
application of the solver.
Furthermore, we explore symmetry breaking for answer set programming in two
domains: first, constraint answer set programming as a novel approach to
represent and solve constraint satisfaction problems, and second, distributed
nonmonotonic multi-context systems. In particular, we formulate a
translation-based approach to constraint answer set solving which allows for
the application of our symmetry detection and symmetry breaking methods. To
compare their performance with a-priori symmetry breaking techniques, we also
contribute a decomposition of the global value precedence constraint that
enforces domain consistency on the original constraint via the unit-propagation
of an answer set solver. We evaluate both options in an empirical analysis. In
the context of distributed nonmonotonic multi-context system, we develop an
algorithm for distributed symmetry detection and also carry over
symmetry-breaking constraints for distributed answer set programming.Comment: Diploma thesis. Vienna University of Technology, August 201
Exploiting single-cycle symmetries in branch-and-prune algorithms
The final publication is available at link.springer.comAs a first attempt to exploit symmetries in continuous constraint problems, we focus on permutations of the variables consisting of one single cycle. We propose a procedure that takes advantage of these symmetries by interacting with a Branch-and-Prune algorithm without interfering with it. A key concept in this procedure are the classes of symmetric boxes formed by bisecting a n-dimensional cube at the same point in all dimensions at the same time. We quantify these classes as a function of n. Moreover, we propose a simple algorithm to generate the representatives of all these classes for any number of variables at very high rates. A problem example from the chemical field and a kinematics solver are used to show the performance of the approach in practice.Peer ReviewedPostprint (author's final draft
Exploiting single-cycle symmetries in branch-and-prune algorithms
As a ïŹrst attempt to exploit symmetries in continuous con- straint problems, we focus on permutations of the variables consisting of one single cycle. We propose a procedure that takes advantage of these symmetries by interacting with a Branch-and-Prune algorithm without interfering with it. A key concept in this procedure are the classes of symmetric boxes formed by bisecting a n-dimensional cube at the same point in all dimensions at the same time. We quantify these classes as a function of n. Moreover, we propose a simple algorithm to generate the representatives of all these classes for any number of variables at very high rates. A problem example from the chemical ïŹeld and a kinematics solver are used to show the performance of the approach in practice.Peer Reviewe
Symmetry-reinforced Nogood Recording from Restarts
dans le cadre de CP'11International audienceNogood recording from restarts is a form of lightweight learn- ing that combines nogood recording with a restart strategy. At the end of each run, nogoods are extracted from the current (rightmost) branch of the search tree. These nogoods can be used to prevent parts of the search space from being explored more than once. In this paper, we propose to reinforce nogood recording (from restarts) by exploiting symmetries: every time the solver has to be restarted, not only the nogoods that are extracted from the current branch are recorded, but also some additional nogoods that can be computed by means of the previously identi ed problem symmetries. This mechanism of computing symmetric nogoods can be iterated until a xed-point is reached, and controlled (if necessary) by limiting the number and/or the size of recorded nogoods
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