37,700 research outputs found
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
Low Scale Non-universal, Non-anomalous U(1)'_F in a Minimal Supersymmetric Standard Model
We propose a non-universal U(1)'_F symmetry combined with the Minimal
Supersymmetric Standard Model. All anomaly cancellation conditions are
satisfied without exotic fields other than three right-handed neutrinos.
Because our model allows all three generations of chiral superfields to have
different U(1)'_F charges, upon the breaking of the U(1)'_F symmetry at a low
scale, realistic masses and mixing angles in both the quark and lepton sectors
are obtained. In our model, neutrinos are predicted to be Dirac fermions and
their mass ordering is of the inverted hierarchy type. The U(1)'_F charges of
the chiral super-fields also naturally suppress the mu term and automatically
forbid baryon number and lepton number violating operators. While all
flavor-changing neutral current constraints in the down quark and charged
lepton sectors can be satisfied, we find that constraint from D0-D0bar turns
out to be much more stringent than the constraints from the precision
electroweak data.Comment: 21 pages, 2 figures; v2: discussion on sparticle mass spectrum
included, 27 pages, 2 figure
Combining Symmetry Breaking and Global Constraints
Abstract. We propose a new family of constraints which combine together lexicographical ordering constraints for symmetry breaking with other common global constraints. We give a general purpose propagator for this family of constraints, and show how to improve its complexity by exploiting properties of the included global constraints.
Order by disorder in a four flavor Mott-insulator on the fcc lattice
The classical ground states of the SU(4) Heisenberg model on the face
centered cubic lattice constitute a highly degenerate manifold. We explicitly
construct all the classical ground states of the model. To describe quantum
fluctuations above these classical states, we apply linear flavor-wave theory.
At zero temperature, the bosonic flavor waves select the simplest of these
SU(4) symmetry breaking states, the four-sublattice ordered state defined by
the cubic unit cell of the fcc lattice. Due to geometrical constraints, flavor
waves interact along specific planes only, thus rendering the system
effectively two dimensional and forbidding ordering at finite temperatures. We
argue that longer range interactions generated by quantum fluctuations can
shift the transition to finite temperatures
Filtering Algorithms for the Multiset Ordering Constraint
Constraint programming (CP) has been used with great success to tackle a wide
variety of constraint satisfaction problems which are computationally
intractable in general. Global constraints are one of the important factors
behind the success of CP. In this paper, we study a new global constraint, the
multiset ordering constraint, which is shown to be useful in symmetry breaking
and searching for leximin optimal solutions in CP. We propose efficient and
effective filtering algorithms for propagating this global constraint. We show
that the algorithms are sound and complete and we discuss possible extensions.
We also consider alternative propagation methods based on existing constraints
in CP toolkits. Our experimental results on a number of benchmark problems
demonstrate that propagating the multiset ordering constraint via a dedicated
algorithm can be very beneficial
Symmetry Breaking Constraints: Recent Results
Symmetry is an important problem in many combinatorial problems. One way of
dealing with symmetry is to add constraints that eliminate symmetric solutions.
We survey recent results in this area, focusing especially on two common and
useful cases: symmetry breaking constraints for row and column symmetry, and
symmetry breaking constraints for eliminating value symmetryComment: To appear in Proceedings of Twenty-Sixth Conference on Artificial
Intelligence (AAAI-12
On The Complexity and Completeness of Static Constraints for Breaking Row and Column Symmetry
We consider a common type of symmetry where we have a matrix of decision
variables with interchangeable rows and columns. A simple and efficient method
to deal with such row and column symmetry is to post symmetry breaking
constraints like DOUBLELEX and SNAKELEX. We provide a number of positive and
negative results on posting such symmetry breaking constraints. On the positive
side, we prove that we can compute in polynomial time a unique representative
of an equivalence class in a matrix model with row and column symmetry if the
number of rows (or of columns) is bounded and in a number of other special
cases. On the negative side, we show that whilst DOUBLELEX and SNAKELEX are
often effective in practice, they can leave a large number of symmetric
solutions in the worst case. In addition, we prove that propagating DOUBLELEX
completely is NP-hard. Finally we consider how to break row, column and value
symmetry, correcting a result in the literature about the safeness of combining
different symmetry breaking constraints. We end with the first experimental
study on how much symmetry is left by DOUBLELEX and SNAKELEX on some benchmark
problems.Comment: To appear in the Proceedings of the 16th International Conference on
Principles and Practice of Constraint Programming (CP 2010
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