17 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
Decompositions of Grammar Constraints
A wide range of constraints can be compactly specified using automata or
formal languages. In a sequence of recent papers, we have shown that an
effective means to reason with such specifications is to decompose them into
primitive constraints. We can then, for instance, use state of the art SAT
solvers and profit from their advanced features like fast unit propagation,
clause learning, and conflict-based search heuristics. This approach holds
promise for solving combinatorial problems in scheduling, rostering, and
configuration, as well as problems in more diverse areas like bioinformatics,
software testing and natural language processing. In addition, decomposition
may be an effective method to propagate other global constraints.Comment: Proceedings of the Twenty-Third AAAI Conference on Artificial
Intelligenc
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
Symmetry-breaking Answer Set Solving
In the context of Answer Set Programming, this paper investigates
symmetry-breaking to eliminate symmetric parts of the search space and,
thereby, simplify the solution process. We propose a reduction of disjunctive
logic programs to a coloured digraph such that permutational symmetries can be
constructed from graph automorphisms. Symmetries are then broken by introducing
symmetry-breaking constraints. For this purpose, we formulate a preprocessor
that integrates a graph automorphism system. Experiments demonstrate its
computational impact.Comment: Proceedings of ICLP'10 Workshop on Answer Set Programming and Other
Computing Paradig
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
Symmetries of Symmetry Breaking Constraints
Symmetry is an important feature of many constraint programs. We show that
any symmetry acting on a set of symmetry breaking constraints can be used to
break symmetry. Different symmetries pick out different solutions in each
symmetry class. We use these observations in two methods for eliminating
symmetry from a problem. These methods are designed to have many of the
advantages of symmetry breaking methods that post static symmetry breaking
constraint without some of the disadvantages. In particular, the two methods
prune the search space using fast and efficient propagation of posted
constraints, whilst reducing the conflict between symmetry breaking and
branching heuristics. Experimental results show that the two methods perform
well on some standard benchmarks.Comment: To appear in the Proceedings of the Ninth International Workshop on
Symmetry and Constraint Satisfaction Problems, held alongside the 15th
International Conference on Principles and Practice of Constraint Programming
(CP 2009), Lisbon, Portuga
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